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

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

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

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

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

Multiply (-6 + 5x) * (3 + 3x)
(-6(3 + 3x) + 5x * (3 + 3x)) = 0
((3 * -6 + 3x * -6) + 5x * (3 + 3x)) = 0
((-18 + -18x) + 5x * (3 + 3x)) = 0
(-18 + -18x + (3 * 5x + 3x * 5x)) = 0
(-18 + -18x + (15x + 15x2)) = 0

Combine like terms: -18x + 15x = -3x
(-18 + -3x + 15x2) = 0

Solving
-18 + -3x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -1x + 5x2) = 0

Factor a trinomial.
3((-1 + -1x)(6 + -5x)) = 0

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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
Solution
x = {-1, 1.2}