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

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

Simplifying
(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((1 + -2x)(2 + x)) = 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 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {0.5, -2}