(8x-6)(2x+9)=0

Solution for (8x-6)(2x+9)=0 equation:

Simplifying
(8x + -6)(2x + 9) = 0

Reorder the terms:
(-6 + 8x)(2x + 9) = 0

Reorder the terms:
(-6 + 8x)(9 + 2x) = 0

Multiply (-6 + 8x) * (9 + 2x)
(-6(9 + 2x) + 8x * (9 + 2x)) = 0
((9 * -6 + 2x * -6) + 8x * (9 + 2x)) = 0
((-54 + -12x) + 8x * (9 + 2x)) = 0
(-54 + -12x + (9 * 8x + 2x * 8x)) = 0
(-54 + -12x + (72x + 16x2)) = 0

Combine like terms: -12x + 72x = 60x
(-54 + 60x + 16x2) = 0

Solving
-54 + 60x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + 30x + 8x2) = 0

Factor a trinomial.
2((-9 + -2x)(3 + -4x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5
Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-4.5, 0.75}