x(x-3)=180

Solution for x(x-3)=180 equation:

Simplifying
x(x + -3) = 180

Reorder the terms:
x(-3 + x) = 180
(-3 * x + x * x) = 180
(-3x + x2) = 180

Solving
-3x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -3x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -3x + x2 = 0

Factor a trinomial.
(-12 + -1x)(15 + -1x) = 0

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-12, 15}