(6x+3)(2x-6)=0

Solution for (6x+3)(2x-6)=0 equation:

Simplifying
(6x + 3)(2x + -6) = 0

Reorder the terms:
(3 + 6x)(2x + -6) = 0

Reorder the terms:
(3 + 6x)(-6 + 2x) = 0

Multiply (3 + 6x) * (-6 + 2x)
(3(-6 + 2x) + 6x * (-6 + 2x)) = 0
((-6 * 3 + 2x * 3) + 6x * (-6 + 2x)) = 0
((-18 + 6x) + 6x * (-6 + 2x)) = 0
(-18 + 6x + (-6 * 6x + 2x * 6x)) = 0
(-18 + 6x + (-36x + 12x2)) = 0

Combine like terms: 6x + -36x = -30x
(-18 + -30x + 12x2) = 0

Solving
-18 + -30x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + -5x + 2x2) = 0

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

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.5, 3}