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On line Solution of Monovariate Equation：
    Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
    It supports equations that contain mathematical functions.
    Current location：Equations > Monovariate Equation > The history of univariate equation calculation > Answer

    Overview: 1 questions will be solved this time.Among them
           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation [1+(k)]*{[12-8(k)]/{[1-2(k)]*[1-2(k)]}} = 60 .
    Question type: Equation
    Solution:Original question:
     (1 + ( k ))((12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k )))) = 60
    Remove a bracket on the left of the equation:：
     1((12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k )))) + ( k )((12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k )))) = 60
    Remove a bracket on the left of the equation:
     1(12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k ))) + ( k )((12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k )))) = 60
     Multiply both sides of the equation by:((1 − 2( k ))(1 − 2( k )))
     1(12 − 8( k )) + ( k )((12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k ))))((1 − 2( k ))(1 − 2( k ))) = 60((1 − 2( k ))(1 − 2( k )))
    Remove a bracket on the left of the equation:
     1 × 12 − 1 × 8( k ) + ( k )((12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k ))))((1 − 2( k ))(1 − 2( k ))) = 60((1 − 2( k ))(1 − 2( k )))
    Remove a bracket on the right of the equation:：
     1 × 12 − 1 × 8( k ) + ( k )((12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k ))))((1 − 2( k ))(1 − 2( k ))) = 60(1 − 2( k ))(1 − 2( k ))
    The equation is reduced to :
     12 − 8( k ) + ( k )((12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k ))))((1 − 2( k ))(1 − 2( k ))) = 60(1 − 2( k ))(1 − 2( k ))
    Remove a bracket on the left of the equation:
     12 − 8 k + ( k )((12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k ))))((1 − 2( k ))(1 − 2( k ))) = 60(1 − 2( k ))(1 − 2( k ))
    Remove a bracket on the right of the equation:：
     12 − 8 k + ( k )((12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k ))))((1 − 2( k ))(1 − 2( k ))) = 60 × 1(1 − 2( k )) − 60 × 2( k )(1 − 2( k ))
    The equation is reduced to :
     12 − 8 k + ( k )((12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k ))))((1 − 2( k ))(1 − 2( k ))) = 60(1 − 2( k )) − 120( k )(1 − 2( k ))
    Remove a bracket on the left of the equation:
     12 − 8 k + k ((12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k ))))((1 − 2( k ))(1 − 2( k ))) = 60(1 − 2( k )) − 120( k )(1 − 2( k ))
    Remove a bracket on the right of the equation:：
     12 − 8 k + k ((12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k ))))((1 − 2( k ))(1 − 2( k ))) = 60 × 1 − 60 × 2( k ) − 120( k )(1 − 2( k ))
    The equation is reduced to :
     12 − 8 k + k ((12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k ))))((1 − 2( k ))(1 − 2( k ))) = 60 − 120( k ) − 120( k )(1 − 2( k ))
    Remove a bracket on the left of the equation:
     12 − 8 k + k (12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k ))) × ((1 − 2( k ))(1 − 2( k ))) = 60 − 120( k ) − 120( k )(1 − 2( k ))
    Remove a bracket on the right of the equation:：
     12 − 8 k + k (12 − 8( k )) ÷ ((1 − 2( k ))(1 − 2( k ))) × ((1 − 2( k ))(1 − 2( k ))) = 60 − 120 k − 120( k )(1 − 2( k ))
     Multiply both sides of the equation by:((1 − 2( k ))(1 − 2( k )))
     12((1 − 2( k ))(1 − 2( k ))) − 8 k ((1 − 2( k ))(1 − 2( k ))) + k (12 − 8( k ))((1 − 2( k ))(1 − 2( k ))) = 60((1 − 2( k ))(1 − 2( k ))) − 120 k ((1 − 2( k ))(1 − 2( k ))) − 120( k )(1 − 2( k ))((1 − 2( k ))(1 − 2( k )))
    Remove a bracket on the left of the equation:
     12(1 − 2( k ))(1 − 2( k )) − 8 k ((1 − 2( k ))(1 − 2( k ))) + k (12 − 8( k ))((1 − 2( k ))(1 − 2( k ))) = 60((1 − 2( k ))(1 − 2( k ))) − 120 k ((1 − 2( k ))(1 − 2( k ))) − 120( k )(1 − 2( k ))((1 − 2( k ))(1 − 2( k )))
    Remove a bracket on the right of the equation:：
     12(1 − 2( k ))(1 − 2( k )) − 8 k ((1 − 2( k ))(1 − 2( k ))) + k (12 − 8( k ))((1 − 2( k ))(1 − 2( k ))) = 60(1 − 2( k ))(1 − 2( k )) − 120 k ((1 − 2( k ))(1 − 2( k ))) − 120( k )(1 − 2( k ))((1 − 2( k ))(1 − 2( k )))
    Remove a bracket on the left of the equation:
     12 × 1(1 − 2( k )) − 12 × 2( k )(1 − 2( k )) − 8 k ((1 − 2( k ))(1 − 2( k ))) + k (12 − 8( k )) = 60(1 − 2( k ))(1 − 2( k )) − 120 k ((1 − 2( k ))(1 − 2( k ))) − 120( k )(1 − 2( k ))((1 − 2( k ))(1 − 2( k )))
    Remove a bracket on the right of the equation:：
     12 × 1(1 − 2( k )) − 12 × 2( k )(1 − 2( k )) − 8 k ((1 − 2( k ))(1 − 2( k ))) + k (12 − 8( k )) = 60 × 1(1 − 2( k )) − 60 × 2( k )(1 − 2( k )) − 120 k ((1 − 2( k ))(1 − 2( k ))) − 120( k )
    The equation is reduced to :
     12(1 − 2( k )) − 24( k )(1 − 2( k )) − 8 k ((1 − 2( k ))(1 − 2( k ))) + k (12 − 8( k ))((1 − 2( k ))(1 − 2( k ))) = 60(1 − 2( k )) − 120( k )(1 − 2( k )) − 120 k ((1 − 2( k ))(1 − 2( k ))) − 120( k )(1 − 2( k ))((1 − 2( k ))(1 − 2( k )))
    Remove a bracket on the left of the equation:
     12 × 1 − 12 × 2( k ) − 24( k )(1 − 2( k )) − 8 k ((1 − 2( k ))(1 − 2( k ))) + k = 60(1 − 2( k )) − 120( k )(1 − 2( k )) − 120 k ((1 − 2( k ))(1 − 2( k ))) − 120( k )(1 − 2( k ))((1 − 2( k ))(1 − 2( k )))
    Remove a bracket on the right of the equation:：
     12 × 1 − 12 × 2( k ) − 24( k )(1 − 2( k )) − 8 k ((1 − 2( k ))(1 − 2( k ))) + k = 60 × 1 − 60 × 2( k ) − 120( k )(1 − 2( k )) − 120 k ((1 − 2( k ))(1 − 2( k ))) − 120
    The equation is reduced to :
     12 − 24( k ) − 24( k )(1 − 2( k )) − 8 k ((1 − 2( k ))(1 − 2( k ))) + k (12 − 8( k ))((1 − 2( k ))(1 − 2( k ))) = 60 − 120( k ) − 120( k )(1 − 2( k )) − 120 k ((1 − 2( k ))(1 − 2( k ))) − 120( k )(1 − 2( k ))

    The solution of the equation:
        k1≈0.271817 , keep 6 decimal places
        k2≈0.712054 , keep 6 decimal places    
    There are 2 solution(s).

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