=6(2-5m)-2m(m+2)

Solution for =6(2-5m)-2m(m+2) equation:

Simplifying
0 = 6(2 + -5m) + -2m(m + 2)
0 = (2 * 6 + -5m * 6) + -2m(m + 2)
0 = (12 + -30m) + -2m(m + 2)

Reorder the terms:
0 = 12 + -30m + -2m(2 + m)
0 = 12 + -30m + (2 * -2m + m * -2m)
0 = 12 + -30m + (-4m + -2m2)

Combine like terms: -30m + -4m = -34m
0 = 12 + -34m + -2m2

Solving
0 = 12 + -34m + -2m2

Solving for variable 'm'.

Combine like terms: 0 + -12 = -12
-12 + 34m + 2m2 = 12 + -34m + -2m2 + -12 + 34m + 2m2

Reorder the terms:
-12 + 34m + 2m2 = 12 + -12 + -34m + 34m + -2m2 + 2m2

Combine like terms: 12 + -12 = 0
-12 + 34m + 2m2 = 0 + -34m + 34m + -2m2 + 2m2
-12 + 34m + 2m2 = -34m + 34m + -2m2 + 2m2

Combine like terms: -34m + 34m = 0
-12 + 34m + 2m2 = 0 + -2m2 + 2m2
-12 + 34m + 2m2 = -2m2 + 2m2

Combine like terms: -2m2 + 2m2 = 0
-12 + 34m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 17m + m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 17m + m2)' equal to zero and attempt to solve:

Simplifying
-6 + 17m + m2 = 0

Solving
-6 + 17m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 17m + 6 + m2 = 0 + 6

Reorder the terms:
-6 + 6 + 17m + m2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 17m + m2 = 0 + 6
17m + m2 = 0 + 6

Combine like terms: 0 + 6 = 6
17m + m2 = 6

The m term is 17m.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17m + 72.25 + m2 = 6 + 72.25

Reorder the terms:
72.25 + 17m + m2 = 6 + 72.25

Combine like terms: 6 + 72.25 = 78.25
72.25 + 17m + m2 = 78.25

Factor a perfect square on the left side:
(m + 8.5)(m + 8.5) = 78.25

Calculate the square root of the right side: 8.845903006

Break this problem into two subproblems by setting 
(m + 8.5) equal to 8.845903006 and -8.845903006.

Subproblem 1
m + 8.5 = 8.845903006

Simplifying
m + 8.5 = 8.845903006

Reorder the terms:
8.5 + m = 8.845903006

Solving
8.5 + m = 8.845903006

Solving for variable 'm'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + m = 8.845903006 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + m = 8.845903006 + -8.5
m = 8.845903006 + -8.5

Combine like terms: 8.845903006 + -8.5 = 0.345903006
m = 0.345903006

Simplifying
m = 0.345903006

Subproblem 2
m + 8.5 = -8.845903006

Simplifying
m + 8.5 = -8.845903006

Reorder the terms:
8.5 + m = -8.845903006

Solving
8.5 + m = -8.845903006

Solving for variable 'm'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + m = -8.845903006 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + m = -8.845903006 + -8.5
m = -8.845903006 + -8.5

Combine like terms: -8.845903006 + -8.5 = -17.345903006
m = -17.345903006

Simplifying
m = -17.345903006

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.345903006, -17.345903006}
Solution
m = {0.345903006, -17.345903006}