(9x-6)(8x+1)=0

Solution for (9x-6)(8x+1)=0 equation:

Simplifying
(9x + -6)(8x + 1) = 0

Reorder the terms:
(-6 + 9x)(8x + 1) = 0

Reorder the terms:
(-6 + 9x)(1 + 8x) = 0

Multiply (-6 + 9x) * (1 + 8x)
(-6(1 + 8x) + 9x * (1 + 8x)) = 0
((1 * -6 + 8x * -6) + 9x * (1 + 8x)) = 0
((-6 + -48x) + 9x * (1 + 8x)) = 0
(-6 + -48x + (1 * 9x + 8x * 9x)) = 0
(-6 + -48x + (9x + 72x2)) = 0

Combine like terms: -48x + 9x = -39x
(-6 + -39x + 72x2) = 0

Solving
-6 + -39x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -13x + 24x2) = 0

Factor a trinomial.
3((-1 + -8x)(2 + -3x)) = 0

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

Simplifying
-1 + -8x = 0

Solving
-1 + -8x = 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 + -8x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8x = 0 + 1
-8x = 0 + 1

Combine like terms: 0 + 1 = 1
-8x = 1

Divide each side by '-8'.
x = -0.125

Simplifying
x = -0.125
Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-0.125, 0.6666666667}