(x^2+12x)+(3x^2+20)=180

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Solution for (x^2+12x)+(3x^2+20)=180 equation: 


Simplifying
(x2 + 12x) + (3x2 + 20) = 180

Reorder the terms:
(12x + x2) + (3x2 + 20) = 180

Remove parenthesis around (12x + x2)
12x + x2 + (3x2 + 20) = 180

Reorder the terms:
12x + x2 + (20 + 3x2) = 180

Remove parenthesis around (20 + 3x2)
12x + x2 + 20 + 3x2 = 180

Reorder the terms:
20 + 12x + x2 + 3x2 = 180

Combine like terms: x2 + 3x2 = 4x2
20 + 12x + 4x2 = 180

Solving
20 + 12x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
20 + -180 + 12x + 4x2 = 180 + -180

Combine like terms: 20 + -180 = -160
-160 + 12x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-160 + 12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-40 + 3x + x2) = 0

Factor a trinomial.
4((-8 + -1x)(5 + -1x)) = 0

Ignore the factor 4.

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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

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

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

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

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

Simplifying
x = 5
Solution
x = {-8, 5}

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