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

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

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

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

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

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

Combine like terms: -3x + 1x = -2x
-2(-3 + -2x + x2) = 0
(-3 * -2 + -2x * -2 + x2 * -2) = 0
(6 + 4x + -2x2) = 0

Solving
6 + 4x + -2x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {3, -1}