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

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

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

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

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

Multiply (-3 + 9x) * (3 + 8x)
(-3(3 + 8x) + 9x * (3 + 8x)) = 0
((3 * -3 + 8x * -3) + 9x * (3 + 8x)) = 0
((-9 + -24x) + 9x * (3 + 8x)) = 0
(-9 + -24x + (3 * 9x + 8x * 9x)) = 0
(-9 + -24x + (27x + 72x2)) = 0

Combine like terms: -24x + 27x = 3x
(-9 + 3x + 72x2) = 0

Solving
-9 + 3x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + x + 24x2) = 0

Factor a trinomial.
3((-3 + -8x)(1 + -3x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + -8x)' equal to zero and attempt to solve:

Simplifying
-3 + -8x = 0

Solving
-3 + -8x = 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 + -8x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8x = 0 + 3
-8x = 0 + 3

Combine like terms: 0 + 3 = 3
-8x = 3

Divide each side by '-8'.
x = -0.375

Simplifying
x = -0.375
Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-0.375, 0.3333333333}