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 + x2) = 0

Factor a trinomial.
2((-3 + -1x)(1 + -1x)) = 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 + -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
Solution
x = {-3, 1}