x(x-3)=108

Solution for x(x-3)=108 equation:

Simplifying
x(x + -3) = 108

Reorder the terms:
x(-3 + x) = 108
(-3 * x + x * x) = 108
(-3x + x2) = 108

Solving
-3x + x2 = 108

Solving for variable 'x'.

Reorder the terms:
-108 + -3x + x2 = 108 + -108

Combine like terms: 108 + -108 = 0
-108 + -3x + x2 = 0

Factor a trinomial.
(-9 + -1x)(12 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
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
Solution
x = {-9, 12}