(9x+2)(-6x+3)=0

Solution for (9x+2)(-6x+3)=0 equation:

Simplifying
(9x + 2)(-6x + 3) = 0

Reorder the terms:
(2 + 9x)(-6x + 3) = 0

Reorder the terms:
(2 + 9x)(3 + -6x) = 0

Multiply (2 + 9x) * (3 + -6x)
(2(3 + -6x) + 9x * (3 + -6x)) = 0
((3 * 2 + -6x * 2) + 9x * (3 + -6x)) = 0
((6 + -12x) + 9x * (3 + -6x)) = 0
(6 + -12x + (3 * 9x + -6x * 9x)) = 0
(6 + -12x + (27x + -54x2)) = 0

Combine like terms: -12x + 27x = 15x
(6 + 15x + -54x2) = 0

Solving
6 + 15x + -54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 5x + -18x2) = 0

Factor a trinomial.
3((1 + -2x)(2 + 9x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
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 = {0.5, -0.2222222222}