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

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

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

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

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

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

Combine like terms: -18x + 9x = -9x
(-54 + -9x + 3x2) = 0

Solving
-54 + -9x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + -3x + x2) = 0

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

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-3, 6}