2(m-6)(m-6)-45=53

Solution for 2(m-6)(m-6)-45=53 equation:

Simplifying
2(m + -6)(m + -6) + -45 = 53

Reorder the terms:
2(-6 + m)(m + -6) + -45 = 53

Reorder the terms:
2(-6 + m)(-6 + m) + -45 = 53

Multiply (-6 + m) * (-6 + m)
2(-6(-6 + m) + m(-6 + m)) + -45 = 53
2((-6 * -6 + m * -6) + m(-6 + m)) + -45 = 53
2((36 + -6m) + m(-6 + m)) + -45 = 53
2(36 + -6m + (-6 * m + m * m)) + -45 = 53
2(36 + -6m + (-6m + m2)) + -45 = 53

Combine like terms: -6m + -6m = -12m
2(36 + -12m + m2) + -45 = 53
(36 * 2 + -12m * 2 + m2 * 2) + -45 = 53
(72 + -24m + 2m2) + -45 = 53

Reorder the terms:
72 + -45 + -24m + 2m2 = 53

Combine like terms: 72 + -45 = 27
27 + -24m + 2m2 = 53

Solving
27 + -24m + 2m2 = 53

Solving for variable 'm'.

Reorder the terms:
27 + -53 + -24m + 2m2 = 53 + -53

Combine like terms: 27 + -53 = -26
-26 + -24m + 2m2 = 53 + -53

Combine like terms: 53 + -53 = 0
-26 + -24m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + -12m + m2) = 0

Factor a trinomial.
2((-1 + -1m)(13 + -1m)) = 0

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

Simplifying
-1 + -1m = 0

Solving
-1 + -1m = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1m = 0 + 1

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

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

Divide each side by '-1'.
m = -1

Simplifying
m = -1
Subproblem 2
Set the factor '(13 + -1m)' equal to zero and attempt to solve:

Simplifying
13 + -1m = 0

Solving
13 + -1m = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1m = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1m = 0 + -13
-1m = 0 + -13

Combine like terms: 0 + -13 = -13
-1m = -13

Divide each side by '-1'.
m = 13

Simplifying
m = 13
Solution
m = {-1, 13}