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

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

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

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

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

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

Combine like terms: 27x + 12x = 39x
(6 + 39x + 54x2) = 0

Solving
6 + 39x + 54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 13x + 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}