(3x-9)(3x+6)=0

Solution for (3x-9)(3x+6)=0 equation:

Simplifying
(3x + -9)(3x + 6) = 0

Reorder the terms:
(-9 + 3x)(3x + 6) = 0

Reorder the terms:
(-9 + 3x)(6 + 3x) = 0

Multiply (-9 + 3x) * (6 + 3x)
(-9(6 + 3x) + 3x * (6 + 3x)) = 0
((6 * -9 + 3x * -9) + 3x * (6 + 3x)) = 0
((-54 + -27x) + 3x * (6 + 3x)) = 0
(-54 + -27x + (6 * 3x + 3x * 3x)) = 0
(-54 + -27x + (18x + 9x2)) = 0

Combine like terms: -27x + 18x = -9x
(-54 + -9x + 9x2) = 0

Solving
-54 + -9x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-6 + -1x + x2) = 0

Factor a trinomial.
9((-2 + -1x)(3 + -1x)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2, 3}