2m^2-2m*3=6(m-3)+4

Solution for 2m^2-2m*3=6(m-3)+4 equation:

Simplifying
2m2 + -2m * 3 = 6(m + -3) + 4

Reorder the terms for easier multiplication:
2m2 + -2 * 3m = 6(m + -3) + 4

Multiply -2 * 3
2m2 + -6m = 6(m + -3) + 4

Reorder the terms:
-6m + 2m2 = 6(m + -3) + 4

Reorder the terms:
-6m + 2m2 = 6(-3 + m) + 4
-6m + 2m2 = (-3 * 6 + m * 6) + 4
-6m + 2m2 = (-18 + 6m) + 4

Reorder the terms:
-6m + 2m2 = -18 + 4 + 6m

Combine like terms: -18 + 4 = -14
-6m + 2m2 = -14 + 6m

Solving
-6m + 2m2 = -14 + 6m

Solving for variable 'm'.

Reorder the terms:
14 + -6m + -6m + 2m2 = -14 + 6m + 14 + -6m

Combine like terms: -6m + -6m = -12m
14 + -12m + 2m2 = -14 + 6m + 14 + -6m

Reorder the terms:
14 + -12m + 2m2 = -14 + 14 + 6m + -6m

Combine like terms: -14 + 14 = 0
14 + -12m + 2m2 = 0 + 6m + -6m
14 + -12m + 2m2 = 6m + -6m

Combine like terms: 6m + -6m = 0
14 + -12m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -6m + m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + -6m + m2)' equal to zero and attempt to solve:

Simplifying
7 + -6m + m2 = 0

Solving
7 + -6m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -6m + -7 + m2 = 0 + -7

Reorder the terms:
7 + -7 + -6m + m2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6m + m2 = 0 + -7
-6m + m2 = 0 + -7

Combine like terms: 0 + -7 = -7
-6m + m2 = -7

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 = -7 + 9

Reorder the terms:
9 + -6m + m2 = -7 + 9

Combine like terms: -7 + 9 = 2
9 + -6m + m2 = 2

Factor a perfect square on the left side:
(m + -3)(m + -3) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(m + -3) equal to 1.414213562 and -1.414213562.

Subproblem 1
m + -3 = 1.414213562

Simplifying
m + -3 = 1.414213562

Reorder the terms:
-3 + m = 1.414213562

Solving
-3 + m = 1.414213562

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 = 1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + m = 1.414213562 + 3
m = 1.414213562 + 3

Combine like terms: 1.414213562 + 3 = 4.414213562
m = 4.414213562

Simplifying
m = 4.414213562

Subproblem 2
m + -3 = -1.414213562

Simplifying
m + -3 = -1.414213562

Reorder the terms:
-3 + m = -1.414213562

Solving
-3 + m = -1.414213562

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 = -1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + m = -1.414213562 + 3
m = -1.414213562 + 3

Combine like terms: -1.414213562 + 3 = 1.585786438
m = 1.585786438

Simplifying
m = 1.585786438

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {4.414213562, 1.585786438}
Solution
m = {4.414213562, 1.585786438}