-8+2(x+1)=-4x(x-1)

Solution for -8+2(x+1)=-4x(x-1) equation:

Simplifying
-8 + 2(x + 1) = -4x(x + -1)

Reorder the terms:
-8 + 2(1 + x) = -4x(x + -1)
-8 + (1 * 2 + x * 2) = -4x(x + -1)
-8 + (2 + 2x) = -4x(x + -1)

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

Reorder the terms:
-6 + 2x = -4x(-1 + x)
-6 + 2x = (-1 * -4x + x * -4x)
-6 + 2x = (4x + -4x2)

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

Solving for variable 'x'.

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

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

Combine like terms: 4x + -4x = 0
-6 + -2x + 4x2 = 0 + -4x2 + 4x2
-6 + -2x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-6 + -2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -1x + 2x2) = 0

Factor a trinomial.
2((-1 + -1x)(3 + -2x)) = 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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1, 1.5}