9(2m-3)(2m-3)+8=449

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Solution for 9(2m-3)(2m-3)+8=449 equation: 


Simplifying
9(2m + -3)(2m + -3) + 8 = 449

Reorder the terms:
9(-3 + 2m)(2m + -3) + 8 = 449

Reorder the terms:
9(-3 + 2m)(-3 + 2m) + 8 = 449

Multiply (-3 + 2m) * (-3 + 2m)
9(-3(-3 + 2m) + 2m * (-3 + 2m)) + 8 = 449
9((-3 * -3 + 2m * -3) + 2m * (-3 + 2m)) + 8 = 449
9((9 + -6m) + 2m * (-3 + 2m)) + 8 = 449
9(9 + -6m + (-3 * 2m + 2m * 2m)) + 8 = 449
9(9 + -6m + (-6m + 4m2)) + 8 = 449

Combine like terms: -6m + -6m = -12m
9(9 + -12m + 4m2) + 8 = 449
(9 * 9 + -12m * 9 + 4m2 * 9) + 8 = 449
(81 + -108m + 36m2) + 8 = 449

Reorder the terms:
81 + 8 + -108m + 36m2 = 449

Combine like terms: 81 + 8 = 89
89 + -108m + 36m2 = 449

Solving
89 + -108m + 36m2 = 449

Solving for variable 'm'.

Reorder the terms:
89 + -449 + -108m + 36m2 = 449 + -449

Combine like terms: 89 + -449 = -360
-360 + -108m + 36m2 = 449 + -449

Combine like terms: 449 + -449 = 0
-360 + -108m + 36m2 = 0

Factor out the Greatest Common Factor (GCF), '36'.
36(-10 + -3m + m2) = 0

Factor a trinomial.
36((-2 + -1m)(5 + -1m)) = 0

Ignore the factor 36.

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

Simplifying
-2 + -1m = 0

Solving
-2 + -1m = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1m = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1m = 0 + 2
-1m = 0 + 2

Combine like terms: 0 + 2 = 2
-1m = 2

Divide each side by '-1'.
m = -2

Simplifying
m = -2

Subproblem 2
Set the factor '(5 + -1m)' equal to zero and attempt to solve:

Simplifying
5 + -1m = 0

Solving
5 + -1m = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1m = 0 + -5
-1m = 0 + -5

Combine like terms: 0 + -5 = -5
-1m = -5

Divide each side by '-1'.
m = 5

Simplifying
m = 5
Solution
m = {-2, 5}

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