x+7=(x+1)(x+1)

Solution for x+7=(x+1)(x+1) equation:

Simplifying
x + 7 = (x + 1)(x + 1)

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

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

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

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

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

Solving
7 + x = 1 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
7 + -1 + x + -2x + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: 7 + -1 = 6
6 + x + -2x + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: x + -2x = -1x
6 + -1x + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Reorder the terms:
6 + -1x + -1x2 = 1 + -1 + 2x + -2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
6 + -1x + -1x2 = 0 + 2x + -2x + x2 + -1x2
6 + -1x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
6 + -1x + -1x2 = 0 + x2 + -1x2
6 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + -1x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(3 + x) = 0

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {2, -3}