2(x-3)(x+1)=-8

Solution for 2(x-3)(x+1)=-8 equation:

Simplifying
2(x + -3)(x + 1) = -8

Reorder the terms:
2(-3 + x)(x + 1) = -8

Reorder the terms:
2(-3 + x)(1 + x) = -8

Multiply (-3 + x) * (1 + x)
2(-3(1 + x) + x(1 + x)) = -8
2((1 * -3 + x * -3) + x(1 + x)) = -8
2((-3 + -3x) + x(1 + x)) = -8
2(-3 + -3x + (1 * x + x * x)) = -8
2(-3 + -3x + (1x + x2)) = -8

Combine like terms: -3x + 1x = -2x
2(-3 + -2x + x2) = -8
(-3 * 2 + -2x * 2 + x2 * 2) = -8
(-6 + -4x + 2x2) = -8

Solving
-6 + -4x + 2x2 = -8

Solving for variable 'x'.

Reorder the terms:
-6 + 8 + -4x + 2x2 = -8 + 8

Combine like terms: -6 + 8 = 2
2 + -4x + 2x2 = -8 + 8

Combine like terms: -8 + 8 = 0
2 + -4x + 2x2 = 0

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

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

Ignore the factor 2.
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 '(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 = {1, 1}