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

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

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

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

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

Multiply (-3 + 8x) * (9 + 2x)
(-3(9 + 2x) + 8x * (9 + 2x)) = 0
((9 * -3 + 2x * -3) + 8x * (9 + 2x)) = 0
((-27 + -6x) + 8x * (9 + 2x)) = 0
(-27 + -6x + (9 * 8x + 2x * 8x)) = 0
(-27 + -6x + (72x + 16x2)) = 0

Combine like terms: -6x + 72x = 66x
(-27 + 66x + 16x2) = 0

Solving
-27 + 66x + 16x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -2x)(3 + -8x) = 0

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 + -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
Solution
x = {-4.5, 0.375}