4x^2-180=2x+2

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


Simplifying
4x2 + -180 = 2x + 2

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

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

Solving
-180 + 4x2 = 2 + 2x

Solving for variable 'x'.

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

Combine like terms: -180 + -2 = -182
-182 + -2x + 4x2 = 2 + 2x + -2 + -2x

Reorder the terms:
-182 + -2x + 4x2 = 2 + -2 + 2x + -2x

Combine like terms: 2 + -2 = 0
-182 + -2x + 4x2 = 0 + 2x + -2x
-182 + -2x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-182 + -2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-91 + -1x + 2x2) = 0

Factor a trinomial.
2((-13 + -2x)(7 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
-13 + -2x = 0

Solving
-13 + -2x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2x = 0 + 13
-2x = 0 + 13

Combine like terms: 0 + 13 = 13
-2x = 13

Divide each side by '-2'.
x = -6.5

Simplifying
x = -6.5

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-6.5, 7}

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