(9x+5)(3x-6)=0

Solution for (9x+5)(3x-6)=0 equation:

Simplifying
(9x + 5)(3x + -6) = 0

Reorder the terms:
(5 + 9x)(3x + -6) = 0

Reorder the terms:
(5 + 9x)(-6 + 3x) = 0

Multiply (5 + 9x) * (-6 + 3x)
(5(-6 + 3x) + 9x * (-6 + 3x)) = 0
((-6 * 5 + 3x * 5) + 9x * (-6 + 3x)) = 0
((-30 + 15x) + 9x * (-6 + 3x)) = 0
(-30 + 15x + (-6 * 9x + 3x * 9x)) = 0
(-30 + 15x + (-54x + 27x2)) = 0

Combine like terms: 15x + -54x = -39x
(-30 + -39x + 27x2) = 0

Solving
-30 + -39x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -13x + 9x2) = 0

Factor a trinomial.
3((-5 + -9x)(2 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -9x)' equal to zero and attempt to solve:

Simplifying
-5 + -9x = 0

Solving
-5 + -9x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -9x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -9x = 0 + 5
-9x = 0 + 5

Combine like terms: 0 + 5 = 5
-9x = 5

Divide each side by '-9'.
x = -0.5555555556

Simplifying
x = -0.5555555556
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.5555555556, 2}