-4(x-2)(x+1)=0

Solution for -4(x-2)(x+1)=0 equation:

Simplifying
-4(x + -2)(x + 1) = 0

Reorder the terms:
-4(-2 + x)(x + 1) = 0

Reorder the terms:
-4(-2 + x)(1 + x) = 0

Multiply (-2 + x) * (1 + x)
-4(-2(1 + x) + x(1 + x)) = 0
-4((1 * -2 + x * -2) + x(1 + x)) = 0
-4((-2 + -2x) + x(1 + x)) = 0
-4(-2 + -2x + (1 * x + x * x)) = 0
-4(-2 + -2x + (1x + x2)) = 0

Combine like terms: -2x + 1x = -1x
-4(-2 + -1x + x2) = 0
(-2 * -4 + -1x * -4 + x2 * -4) = 0
(8 + 4x + -4x2) = 0

Solving
8 + 4x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + x + -1x2) = 0

Factor a trinomial.
4((2 + -1x)(1 + x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
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 = {2, -1}