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

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

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

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

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

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

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

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

Add '-2x' to each side of the equation.
1 + 2x + -2x + x2 = 2 + 2x + -2x

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

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

Solving
1 + x2 = 2

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 = 2 + -1

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

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

Simplifying
x2 = 1

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