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

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

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

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

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

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

Combine like terms: -27x + 6x = -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 + -9x)(1 + -2x)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-0.1111111111, 0.5}