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

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

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

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

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

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

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

Solving
6 + -3x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -1x + -1x2) = 0

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

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
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 = {1, -2}