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

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

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

Reorder the terms:
2x + -4x(-2 + x) = 2x + 4
2x + (-2 * -4x + x * -4x) = 2x + 4
2x + (8x + -4x2) = 2x + 4

Combine like terms: 2x + 8x = 10x
10x + -4x2 = 2x + 4

Reorder the terms:
10x + -4x2 = 4 + 2x

Solving
10x + -4x2 = 4 + 2x

Solving for variable 'x'.

Reorder the terms:
-4 + 10x + -2x + -4x2 = 4 + 2x + -4 + -2x

Combine like terms: 10x + -2x = 8x
-4 + 8x + -4x2 = 4 + 2x + -4 + -2x

Reorder the terms:
-4 + 8x + -4x2 = 4 + -4 + 2x + -2x

Combine like terms: 4 + -4 = 0
-4 + 8x + -4x2 = 0 + 2x + -2x
-4 + 8x + -4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-4 + 8x + -4x2 = 0

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

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

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
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
Solution
x = {1, 1}