(9x-1)(6x+3)=0

Solution for (9x-1)(6x+3)=0 equation:

Simplifying
(9x + -1)(6x + 3) = 0

Reorder the terms:
(-1 + 9x)(6x + 3) = 0

Reorder the terms:
(-1 + 9x)(3 + 6x) = 0

Multiply (-1 + 9x) * (3 + 6x)
(-1(3 + 6x) + 9x * (3 + 6x)) = 0
((3 * -1 + 6x * -1) + 9x * (3 + 6x)) = 0
((-3 + -6x) + 9x * (3 + 6x)) = 0
(-3 + -6x + (3 * 9x + 6x * 9x)) = 0
(-3 + -6x + (27x + 54x2)) = 0

Combine like terms: -6x + 27x = 21x
(-3 + 21x + 54x2) = 0

Solving
-3 + 21x + 54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 7x + 18x2) = 0

Factor a trinomial.
3((-1 + -2x)(1 + -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 '(1 + -9x)' equal to zero and attempt to solve:

Simplifying
1 + -9x = 0

Solving
1 + -9x = 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 + -9x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -9x = 0 + -1
-9x = 0 + -1

Combine like terms: 0 + -1 = -1
-9x = -1

Divide each side by '-9'.
x = 0.1111111111

Simplifying
x = 0.1111111111
Solution
x = {-0.5, 0.1111111111}