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

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

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

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

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

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

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

Solving
-72 + -6x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-12 + -1x + x2) = 0

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

Ignore the factor 6.
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 '(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
Solution
x = {-3, 4}