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

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

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

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

Reorder the terms for easier multiplication:
(2(3 + x))(x + -1) = 0
((3 * 2 + x * 2))(x + -1) = 0
((6 + 2x))(x + -1) = 0

Reorder the terms:
(6 + 2x)(-1 + x) = 0

Multiply (6 + 2x) * (-1 + x)
(6(-1 + x) + 2x * (-1 + x)) = 0
((-1 * 6 + x * 6) + 2x * (-1 + x)) = 0
((-6 + 6x) + 2x * (-1 + x)) = 0
(-6 + 6x + (-1 * 2x + x * 2x)) = 0
(-6 + 6x + (-2x + 2x2)) = 0

Combine like terms: 6x + -2x = 4x
(-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}