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

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

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

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

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

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

Combine like terms: 3x + -2x = 1x
-3(-6 + 1x + x2) = 0
(-6 * -3 + 1x * -3 + x2 * -3) = 0
(18 + -3x + -3x2) = 0

Solving
18 + -3x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -1x + -1x2) = 0

Factor a trinomial.
3((2 + -1x)(3 + x)) = 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {2, -3}