7(m-6)m=8

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Solution for 7(m-6)m=8 equation:


Simplifying
7(m + -6) * m = 8

Reorder the terms:
7(-6 + m) * m = 8

Reorder the terms for easier multiplication:
7m(-6 + m) = 8
(-6 * 7m + m * 7m) = 8
(-42m + 7m2) = 8

Solving
-42m + 7m2 = 8

Solving for variable 'm'.

Reorder the terms:
-8 + -42m + 7m2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -42m + 7m2 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
-1.142857143 + -6m + m2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + -6m + 1.142857143 + m2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + -6m + m2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + -6m + m2 = 0 + 1.142857143
-6m + m2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
-6m + m2 = 1.142857143

The m term is -6m.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6m + 9 + m2 = 1.142857143 + 9

Reorder the terms:
9 + -6m + m2 = 1.142857143 + 9

Combine like terms: 1.142857143 + 9 = 10.142857143
9 + -6m + m2 = 10.142857143

Factor a perfect square on the left side:
(m + -3)(m + -3) = 10.142857143

Calculate the square root of the right side: 3.184785259

Break this problem into two subproblems by setting 
(m + -3) equal to 3.184785259 and -3.184785259.

Subproblem 1

m + -3 = 3.184785259 Simplifying m + -3 = 3.184785259 Reorder the terms: -3 + m = 3.184785259 Solving -3 + m = 3.184785259 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = 3.184785259 + 3 Combine like terms: -3 + 3 = 0 0 + m = 3.184785259 + 3 m = 3.184785259 + 3 Combine like terms: 3.184785259 + 3 = 6.184785259 m = 6.184785259 Simplifying m = 6.184785259

Subproblem 2

m + -3 = -3.184785259 Simplifying m + -3 = -3.184785259 Reorder the terms: -3 + m = -3.184785259 Solving -3 + m = -3.184785259 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = -3.184785259 + 3 Combine like terms: -3 + 3 = 0 0 + m = -3.184785259 + 3 m = -3.184785259 + 3 Combine like terms: -3.184785259 + 3 = -0.184785259 m = -0.184785259 Simplifying m = -0.184785259

Solution

The solution to the problem is based on the solutions from the subproblems. m = {6.184785259, -0.184785259}

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