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

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

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

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

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

Multiply (2 + x) * (2 + x)
(2(2 + x) + x(2 + x)) + -1 = 0
((2 * 2 + x * 2) + x(2 + x)) + -1 = 0
((4 + 2x) + x(2 + x)) + -1 = 0
(4 + 2x + (2 * x + x * x)) + -1 = 0
(4 + 2x + (2x + x2)) + -1 = 0

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

Reorder the terms:
4 + -1 + 4x + x2 = 0

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

Solving
3 + 4x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
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 = {-3, -1}