0=x^2+24x-180

Solution for 0=x^2+24x-180 equation:

Simplifying
0 = x2 + 24x + -180

Reorder the terms:
0 = -180 + 24x + x2

Solving
0 = -180 + 24x + x2

Solving for variable 'x'.

Combine like terms: 0 + 180 = 180
180 + -24x + -1x2 = -180 + 24x + x2 + 180 + -24x + -1x2

Reorder the terms:
180 + -24x + -1x2 = -180 + 180 + 24x + -24x + x2 + -1x2

Combine like terms: -180 + 180 = 0
180 + -24x + -1x2 = 0 + 24x + -24x + x2 + -1x2
180 + -24x + -1x2 = 24x + -24x + x2 + -1x2

Combine like terms: 24x + -24x = 0
180 + -24x + -1x2 = 0 + x2 + -1x2
180 + -24x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
180 + -24x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(30 + x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(30 + x)' equal to zero and attempt to solve:

Simplifying
30 + x = 0

Solving
30 + x = 0

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

Add '-30' to each side of the equation.
30 + -30 + x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + x = 0 + -30
x = 0 + -30

Combine like terms: 0 + -30 = -30
x = -30

Simplifying
x = -30
Solution
x = {6, -30}