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

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

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

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

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

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

Combine like terms: -3x + 12x = 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((-2 + -1x)(1 + -2x)) = 0

Ignore the factor 3.
Subproblem 1
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
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 = {-2, 0.5}