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

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

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

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

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

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

Combine like terms: 16x + 27x = 43x
(6 + 43x + 72x2) = 0

Solving
6 + 43x + 72x2 = 0

Solving for variable 'x'.

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

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 '(2 + 9x)' equal to zero and attempt to solve:

Simplifying
2 + 9x = 0

Solving
2 + 9x = 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 + 9x = 0 + -2

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

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

Divide each side by '9'.
x = -0.2222222222

Simplifying
x = -0.2222222222
Solution
x = {-0.375, -0.2222222222}