(9x-1)(4x+6)=0

Solution for (9x-1)(4x+6)=0 equation:

Simplifying
(9x + -1)(4x + 6) = 0

Reorder the terms:
(-1 + 9x)(4x + 6) = 0

Reorder the terms:
(-1 + 9x)(6 + 4x) = 0

Multiply (-1 + 9x) * (6 + 4x)
(-1(6 + 4x) + 9x * (6 + 4x)) = 0
((6 * -1 + 4x * -1) + 9x * (6 + 4x)) = 0
((-6 + -4x) + 9x * (6 + 4x)) = 0
(-6 + -4x + (6 * 9x + 4x * 9x)) = 0
(-6 + -4x + (54x + 36x2)) = 0

Combine like terms: -4x + 54x = 50x
(-6 + 50x + 36x2) = 0

Solving
-6 + 50x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 25x + 18x2) = 0

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

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

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5
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 = {-1.5, 0.1111111111}