2(x-2)(x+1)=-4

Solution for 2(x-2)(x+1)=-4 equation:

Simplifying
2(x + -2)(x + 1) = -4

Reorder the terms:
2(-2 + x)(x + 1) = -4

Reorder the terms:
2(-2 + x)(1 + x) = -4

Multiply (-2 + x) * (1 + x)
2(-2(1 + x) + x(1 + x)) = -4
2((1 * -2 + x * -2) + x(1 + x)) = -4
2((-2 + -2x) + x(1 + x)) = -4
2(-2 + -2x + (1 * x + x * x)) = -4
2(-2 + -2x + (1x + x2)) = -4

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

Add '4' to each side of the equation.
-4 + -2x + 4 + 2x2 = -4 + 4

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

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

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

Solving
-2x + 2x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
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 = {0, 1}