(3x-6)(2x+1)=0

Solution for (3x-6)(2x+1)=0 equation:

Simplifying
(3x + -6)(2x + 1) = 0

Reorder the terms:
(-6 + 3x)(2x + 1) = 0

Reorder the terms:
(-6 + 3x)(1 + 2x) = 0

Multiply (-6 + 3x) * (1 + 2x)
(-6(1 + 2x) + 3x * (1 + 2x)) = 0
((1 * -6 + 2x * -6) + 3x * (1 + 2x)) = 0
((-6 + -12x) + 3x * (1 + 2x)) = 0
(-6 + -12x + (1 * 3x + 2x * 3x)) = 0
(-6 + -12x + (3x + 6x2)) = 0

Combine like terms: -12x + 3x = -9x
(-6 + -9x + 6x2) = 0

Solving
-6 + -9x + 6x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 3.
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 '(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 = {-0.5, 2}