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

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

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

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

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

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

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

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

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

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

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

Solving
-1 + x2 = 0

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x2 = 0 + 1

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

Combine like terms: 0 + 1 = 1
x2 = 1

Simplifying
x2 = 1

Take the square root of each side:
x = {-1, 1}