(x+2)-(x^2-4)=0

Solution for (x+2)-(x^2-4)=0 equation:

Simplifying
(x + 2) + -1(x2 + -4) = 0

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

Remove parenthesis around (2 + x)
2 + x + -1(x2 + -4) = 0

Reorder the terms:
2 + x + -1(-4 + x2) = 0
2 + x + (-4 * -1 + x2 * -1) = 0
2 + x + (4 + -1x2) = 0

Reorder the terms:
2 + 4 + x + -1x2 = 0

Combine like terms: 2 + 4 = 6
6 + x + -1x2 = 0

Solving
6 + x + -1x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
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 = {3, -2}