(x+2)(x+2)+x^2=4

Solution for (x+2)(x+2)+x^2=4 equation:

Simplifying
(x + 2)(x + 2) + x2 = 4

Reorder the terms:
(2 + x)(x + 2) + x2 = 4

Reorder the terms:
(2 + x)(2 + x) + x2 = 4

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

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

Combine like terms: x2 + x2 = 2x2
4 + 4x + 2x2 = 4

Add '-4' to each side of the equation.
4 + 4x + -4 + 2x2 = 4 + -4

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

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

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

Solving
4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(2 + x) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {0, -2}