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

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

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

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

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

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

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

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

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

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

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

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

Multiply (2 + x) * (2 + x)
1 + 2x + 2x2 = (2(2 + x) + x(2 + x))
1 + 2x + 2x2 = ((2 * 2 + x * 2) + x(2 + x))
1 + 2x + 2x2 = ((4 + 2x) + x(2 + x))
1 + 2x + 2x2 = (4 + 2x + (2 * x + x * x))
1 + 2x + 2x2 = (4 + 2x + (2x + x2))

Combine like terms: 2x + 2x = 4x
1 + 2x + 2x2 = (4 + 4x + x2)

Solving
1 + 2x + 2x2 = 4 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
1 + -4 + 2x + -4x + 2x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 1 + -4 = -3
-3 + 2x + -4x + 2x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 2x + -4x = -2x
-3 + -2x + 2x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-3 + -2x + 1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Reorder the terms:
-3 + -2x + 1x2 = 4 + -4 + 4x + -4x + x2 + -1x2

Combine like terms: 4 + -4 = 0
-3 + -2x + 1x2 = 0 + 4x + -4x + x2 + -1x2
-3 + -2x + 1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
-3 + -2x + 1x2 = 0 + x2 + -1x2
-3 + -2x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + -2x + 1x2 = 0

Factor a trinomial.
(-1 + -1x)(3 + -1x) = 0

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 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1, 3}