(x+2)(x+2)-1=48

Solution for (x+2)(x+2)-1=48 equation:

Simplifying
(x + 2)(x + 2) + -1 = 48

Reorder the terms:
(2 + x)(x + 2) + -1 = 48

Reorder the terms:
(2 + x)(2 + x) + -1 = 48

Multiply (2 + x) * (2 + x)
(2(2 + x) + x(2 + x)) + -1 = 48
((2 * 2 + x * 2) + x(2 + x)) + -1 = 48
((4 + 2x) + x(2 + x)) + -1 = 48
(4 + 2x + (2 * x + x * x)) + -1 = 48
(4 + 2x + (2x + x2)) + -1 = 48

Combine like terms: 2x + 2x = 4x
(4 + 4x + x2) + -1 = 48

Reorder the terms:
4 + -1 + 4x + x2 = 48

Combine like terms: 4 + -1 = 3
3 + 4x + x2 = 48

Solving
3 + 4x + x2 = 48

Solving for variable 'x'.

Reorder the terms:
3 + -48 + 4x + x2 = 48 + -48

Combine like terms: 3 + -48 = -45
-45 + 4x + x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-45 + 4x + x2 = 0

Factor a trinomial.
(-9 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-9, 5}