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

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

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

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

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

Multiply (6 + -5x) * (3 + 6x)
(6(3 + 6x) + -5x * (3 + 6x)) = 0
((3 * 6 + 6x * 6) + -5x * (3 + 6x)) = 0
((18 + 36x) + -5x * (3 + 6x)) = 0
(18 + 36x + (3 * -5x + 6x * -5x)) = 0
(18 + 36x + (-15x + -30x2)) = 0

Combine like terms: 36x + -15x = 21x
(18 + 21x + -30x2) = 0

Solving
18 + 21x + -30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 7x + -10x2) = 0

Factor a trinomial.
3((6 + -5x)(1 + 2x)) = 0

Ignore the factor 3.
Subproblem 1
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
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 = {1.2, -0.5}