x^2+4+4x-10+x^2+8x+4=180

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Solution for x^2+4+4x-10+x^2+8x+4=180 equation: 


Simplifying
x2 + 4 + 4x + -10 + x2 + 8x + 4 = 180

Reorder the terms:
4 + -10 + 4 + 4x + 8x + x2 + x2 = 180

Combine like terms: 4 + -10 = -6
-6 + 4 + 4x + 8x + x2 + x2 = 180

Combine like terms: -6 + 4 = -2
-2 + 4x + 8x + x2 + x2 = 180

Combine like terms: 4x + 8x = 12x
-2 + 12x + x2 + x2 = 180

Combine like terms: x2 + x2 = 2x2
-2 + 12x + 2x2 = 180

Solving
-2 + 12x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-2 + -180 + 12x + 2x2 = 180 + -180

Combine like terms: -2 + -180 = -182
-182 + 12x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-182 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-91 + 6x + x2) = 0

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

Ignore the factor 2.

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

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 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 + -1x = 0 + 13

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

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

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

Simplifying
x = -13

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 = {-13, 7}

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