12x+8x+27+x^2+28=180

Solution for 12x+8x+27+x^2+28=180 equation:

Simplifying
12x + 8x + 27 + x2 + 28 = 180

Reorder the terms:
27 + 28 + 12x + 8x + x2 = 180

Combine like terms: 27 + 28 = 55
55 + 12x + 8x + x2 = 180

Combine like terms: 12x + 8x = 20x
55 + 20x + x2 = 180

Solving
55 + 20x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
55 + -180 + 20x + x2 = 180 + -180

Combine like terms: 55 + -180 = -125
-125 + 20x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-125 + 20x + x2 = 0

Factor a trinomial.
(-25 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-25 + -1x)' equal to zero and attempt to solve:

Simplifying
-25 + -1x = 0

Solving
-25 + -1x = 0

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

Add '25' to each side of the equation.
-25 + 25 + -1x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1x = 0 + 25
-1x = 0 + 25

Combine like terms: 0 + 25 = 25
-1x = 25

Divide each side by '-1'.
x = -25

Simplifying
x = -25
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 = {-25, 5}