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

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

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

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

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

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

Combine like terms: -72x + 6x = -66x
(-9 + -66x + 48x2) = 0

Solving
-9 + -66x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -22x + 16x2) = 0

Factor a trinomial.
3((-1 + -8x)(3 + -2x)) = 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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-0.125, 1.5}