0=-x^2+24x+180

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

Simplifying
0 = -1x2 + 24x + 180

Reorder the terms:
0 = 180 + 24x + -1x2

Solving
0 = 180 + 24x + -1x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(-6 + -1x)(30 + -1x) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 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 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

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