x^2-32+2x^2-3x-4=180

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Solution for x^2-32+2x^2-3x-4=180 equation: 


Simplifying
x2 + -32 + 2x2 + -3x + -4 = 180

Reorder the terms:
-32 + -4 + -3x + x2 + 2x2 = 180

Combine like terms: -32 + -4 = -36
-36 + -3x + x2 + 2x2 = 180

Combine like terms: x2 + 2x2 = 3x2
-36 + -3x + 3x2 = 180

Solving
-36 + -3x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
-36 + -180 + -3x + 3x2 = 180 + -180

Combine like terms: -36 + -180 = -216
-216 + -3x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-216 + -3x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-72 + -1x + x2) = 0

Factor a trinomial.
3((-8 + -1x)(9 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-8, 9}

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