8m(m-3)=56

Solution for 8m(m-3)=56 equation:

Simplifying
8m(m + -3) = 56

Reorder the terms:
8m(-3 + m) = 56
(-3 * 8m + m * 8m) = 56
(-24m + 8m2) = 56

Solving
-24m + 8m2 = 56

Solving for variable 'm'.

Reorder the terms:
-56 + -24m + 8m2 = 56 + -56

Combine like terms: 56 + -56 = 0
-56 + -24m + 8m2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-7 + -3m + m2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-7 + -3m + m2)' equal to zero and attempt to solve:

Simplifying
-7 + -3m + m2 = 0

Solving
-7 + -3m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -3m + 7 + m2 = 0 + 7

Reorder the terms:
-7 + 7 + -3m + m2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3m + m2 = 0 + 7
-3m + m2 = 0 + 7

Combine like terms: 0 + 7 = 7
-3m + m2 = 7

The m term is -3m.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3m + 2.25 + m2 = 7 + 2.25

Reorder the terms:
2.25 + -3m + m2 = 7 + 2.25

Combine like terms: 7 + 2.25 = 9.25
2.25 + -3m + m2 = 9.25

Factor a perfect square on the left side:
(m + -1.5)(m + -1.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(m + -1.5) equal to 3.041381265 and -3.041381265.

Subproblem 1
m + -1.5 = 3.041381265

Simplifying
m + -1.5 = 3.041381265

Reorder the terms:
-1.5 + m = 3.041381265

Solving
-1.5 + m = 3.041381265

Solving for variable 'm'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + m = 3.041381265 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + m = 3.041381265 + 1.5
m = 3.041381265 + 1.5

Combine like terms: 3.041381265 + 1.5 = 4.541381265
m = 4.541381265

Simplifying
m = 4.541381265

Subproblem 2
m + -1.5 = -3.041381265

Simplifying
m + -1.5 = -3.041381265

Reorder the terms:
-1.5 + m = -3.041381265

Solving
-1.5 + m = -3.041381265

Solving for variable 'm'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + m = -3.041381265 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + m = -3.041381265 + 1.5
m = -3.041381265 + 1.5

Combine like terms: -3.041381265 + 1.5 = -1.541381265
m = -1.541381265

Simplifying
m = -1.541381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {4.541381265, -1.541381265}
Solution
m = {4.541381265, -1.541381265}