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

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

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

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

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

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

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

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {1, -2}