(3x-9)(2x+8)=0

Solution for (3x-9)(2x+8)=0 equation:

Simplifying
(3x + -9)(2x + 8) = 0

Reorder the terms:
(-9 + 3x)(2x + 8) = 0

Reorder the terms:
(-9 + 3x)(8 + 2x) = 0

Multiply (-9 + 3x) * (8 + 2x)
(-9(8 + 2x) + 3x * (8 + 2x)) = 0
((8 * -9 + 2x * -9) + 3x * (8 + 2x)) = 0
((-72 + -18x) + 3x * (8 + 2x)) = 0
(-72 + -18x + (8 * 3x + 2x * 3x)) = 0
(-72 + -18x + (24x + 6x2)) = 0

Combine like terms: -18x + 24x = 6x
(-72 + 6x + 6x2) = 0

Solving
-72 + 6x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-12 + x + x2) = 0

Factor a trinomial.
6((-4 + -1x)(3 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
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 = {-4, 3}