(4x-8)(x+1)=0

Solution for (4x-8)(x+1)=0 equation:

Simplifying
(4x + -8)(x + 1) = 0

Reorder the terms:
(-8 + 4x)(x + 1) = 0

Reorder the terms:
(-8 + 4x)(1 + x) = 0

Multiply (-8 + 4x) * (1 + x)
(-8(1 + x) + 4x * (1 + x)) = 0
((1 * -8 + x * -8) + 4x * (1 + x)) = 0
((-8 + -8x) + 4x * (1 + x)) = 0
(-8 + -8x + (1 * 4x + x * 4x)) = 0
(-8 + -8x + (4x + 4x2)) = 0

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

Solving
-8 + -4x + 4x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
4((-1 + -1x)(2 + -1x)) = 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 + -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
Solution
x = {-1, 2}