0=3(x^2+6x-72)

Solution for 0=3(x^2+6x-72) equation:

Simplifying
0 = 3(x2 + 6x + -72)

Reorder the terms:
0 = 3(-72 + 6x + x2)
0 = (-72 * 3 + 6x * 3 + x2 * 3)
0 = (-216 + 18x + 3x2)

Solving
0 = -216 + 18x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 216 = 216
216 + -18x + -3x2 = -216 + 18x + 3x2 + 216 + -18x + -3x2

Reorder the terms:
216 + -18x + -3x2 = -216 + 216 + 18x + -18x + 3x2 + -3x2

Combine like terms: -216 + 216 = 0
216 + -18x + -3x2 = 0 + 18x + -18x + 3x2 + -3x2
216 + -18x + -3x2 = 18x + -18x + 3x2 + -3x2

Combine like terms: 18x + -18x = 0
216 + -18x + -3x2 = 0 + 3x2 + -3x2
216 + -18x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
216 + -18x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(72 + -6x + -1x2) = 0

Factor a trinomial.
3((6 + -1x)(12 + x)) = 0

Ignore the factor 3.
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 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 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 + x = 0 + -12

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

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

Simplifying
x = -12
Solution
x = {6, -12}