2(4m-7)m=76

Solution for 2(4m-7)m=76 equation:

Simplifying
2(4m + -7) * m = 76

Reorder the terms:
2(-7 + 4m) * m = 76

Reorder the terms for easier multiplication:
2m(-7 + 4m) = 76
(-7 * 2m + 4m * 2m) = 76
(-14m + 8m2) = 76

Solving
-14m + 8m2 = 76

Solving for variable 'm'.

Reorder the terms:
-76 + -14m + 8m2 = 76 + -76

Combine like terms: 76 + -76 = 0
-76 + -14m + 8m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-38 + -7m + 4m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-38 + -7m + 4m2)' equal to zero and attempt to solve:

Simplifying
-38 + -7m + 4m2 = 0

Solving
-38 + -7m + 4m2 = 0

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

Divide each side by '4'.
-9.5 + -1.75m + m2 = 0

Move the constant term to the right:

Add '9.5' to each side of the equation.
-9.5 + -1.75m + 9.5 + m2 = 0 + 9.5

Reorder the terms:
-9.5 + 9.5 + -1.75m + m2 = 0 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + -1.75m + m2 = 0 + 9.5
-1.75m + m2 = 0 + 9.5

Combine like terms: 0 + 9.5 = 9.5
-1.75m + m2 = 9.5

The m term is -1.75m.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75m + 0.765625 + m2 = 9.5 + 0.765625

Reorder the terms:
0.765625 + -1.75m + m2 = 9.5 + 0.765625

Combine like terms: 9.5 + 0.765625 = 10.265625
0.765625 + -1.75m + m2 = 10.265625

Factor a perfect square on the left side:
(m + -0.875)(m + -0.875) = 10.265625

Calculate the square root of the right side: 3.204001404

Break this problem into two subproblems by setting 
(m + -0.875) equal to 3.204001404 and -3.204001404.

Subproblem 1
m + -0.875 = 3.204001404

Simplifying
m + -0.875 = 3.204001404

Reorder the terms:
-0.875 + m = 3.204001404

Solving
-0.875 + m = 3.204001404

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '0.875' to each side of the equation.
-0.875 + 0.875 + m = 3.204001404 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + m = 3.204001404 + 0.875
m = 3.204001404 + 0.875

Combine like terms: 3.204001404 + 0.875 = 4.079001404
m = 4.079001404

Simplifying
m = 4.079001404

Subproblem 2
m + -0.875 = -3.204001404

Simplifying
m + -0.875 = -3.204001404

Reorder the terms:
-0.875 + m = -3.204001404

Solving
-0.875 + m = -3.204001404

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '0.875' to each side of the equation.
-0.875 + 0.875 + m = -3.204001404 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + m = -3.204001404 + 0.875
m = -3.204001404 + 0.875

Combine like terms: -3.204001404 + 0.875 = -2.329001404
m = -2.329001404

Simplifying
m = -2.329001404

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {4.079001404, -2.329001404}
Solution
m = {4.079001404, -2.329001404}