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

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

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

Remove parenthesis around (2 + -2x)
(2 + -2x + -1(1 + -1x))(1 + x) + 2x(x + 1) = 0
(2 + -2x + (1 * -1 + -1x * -1))(1 + x) + 2x(x + 1) = 0
(2 + -2x + (-1 + 1x))(1 + x) + 2x(x + 1) = 0

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

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

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

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

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

Reorder the terms:
1 + -1x2 + 2x(1 + x) = 0
1 + -1x2 + (1 * 2x + x * 2x) = 0
1 + -1x2 + (2x + 2x2) = 0

Reorder the terms:
1 + 2x + -1x2 + 2x2 = 0

Combine like terms: -1x2 + 2x2 = 1x2
1 + 2x + 1x2 = 0

Solving
1 + 2x + 1x2 = 0

Solving for variable 'x'.

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

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 + 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 = {-1, -1}