-2m^2-m+12=-3m+6m

Solution for -2m^2-m+12=-3m+6m equation:

Simplifying
-2m2 + -1m + 12 = -3m + 6m

Reorder the terms:
12 + -1m + -2m2 = -3m + 6m

Combine like terms: -3m + 6m = 3m
12 + -1m + -2m2 = 3m

Solving
12 + -1m + -2m2 = 3m

Solving for variable 'm'.

Reorder the terms:
12 + -1m + -3m + -2m2 = 3m + -3m

Combine like terms: -1m + -3m = -4m
12 + -4m + -2m2 = 3m + -3m

Combine like terms: 3m + -3m = 0
12 + -4m + -2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -2m + -1m2) = 0

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

Simplifying
6 + -2m + -1m2 = 0

Solving
6 + -2m + -1m2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + 2m + m2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 2m + 6 + m2 = 0 + 6

Reorder the terms:
-6 + 6 + 2m + m2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 2m + m2 = 0 + 6
2m + m2 = 0 + 6

Combine like terms: 0 + 6 = 6
2m + m2 = 6

The m term is 2m.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2m + 1 + m2 = 6 + 1

Reorder the terms:
1 + 2m + m2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + 2m + m2 = 7

Factor a perfect square on the left side:
(m + 1)(m + 1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(m + 1) equal to 2.645751311 and -2.645751311.

Subproblem 1
m + 1 = 2.645751311

Simplifying
m + 1 = 2.645751311

Reorder the terms:
1 + m = 2.645751311

Solving
1 + m = 2.645751311

Solving for variable 'm'.

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

Add '-1' to each side of the equation.
1 + -1 + m = 2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + m = 2.645751311 + -1
m = 2.645751311 + -1

Combine like terms: 2.645751311 + -1 = 1.645751311
m = 1.645751311

Simplifying
m = 1.645751311

Subproblem 2
m + 1 = -2.645751311

Simplifying
m + 1 = -2.645751311

Reorder the terms:
1 + m = -2.645751311

Solving
1 + m = -2.645751311

Solving for variable 'm'.

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

Add '-1' to each side of the equation.
1 + -1 + m = -2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + m = -2.645751311 + -1
m = -2.645751311 + -1

Combine like terms: -2.645751311 + -1 = -3.645751311
m = -3.645751311

Simplifying
m = -3.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.645751311, -3.645751311}
Solution
m = {1.645751311, -3.645751311}