x(x-6)=72

Solution for x(x-6)=72 equation:

Simplifying
x(x + -6) = 72

Reorder the terms:
x(-6 + x) = 72
(-6 * x + x * x) = 72
(-6x + x2) = 72

Solving
-6x + x2 = 72

Solving for variable 'x'.

Reorder the terms:
-72 + -6x + x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + -6x + x2 = 0

Factor a trinomial.
(-6 + -1x)(12 + -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 '(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 = {-6, 12}