(12x+72)+(x^2)=180

Solution for (12x+72)+(x^2)=180 equation:

Simplifying
(12x + 72) + (x2) = 180

Reorder the terms:
(72 + 12x) + (x2) = 180

Remove parenthesis around (72 + 12x)
72 + 12x + (x2) = 180
72 + 12x + x2 = 180

Solving
72 + 12x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
72 + -180 + 12x + x2 = 180 + -180

Combine like terms: 72 + -180 = -108
-108 + 12x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-108 + 12x + x2 = 0

Factor a trinomial.
(-18 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-18 + -1x)' equal to zero and attempt to solve:

Simplifying
-18 + -1x = 0

Solving
-18 + -1x = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1x = 0 + 18
-1x = 0 + 18

Combine like terms: 0 + 18 = 18
-1x = 18

Divide each side by '-1'.
x = -18

Simplifying
x = -18
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-18, 6}