(X^2+4)=(24+X)

Solution for (X^2+4)=(24+X) equation:

Simplifying
(X2 + 4) = (24 + X)

Reorder the terms:
(4 + X2) = (24 + X)

Remove parenthesis around (4 + X2)
4 + X2 = (24 + X)

Remove parenthesis around (24 + X)
4 + X2 = 24 + X

Solving
4 + X2 = 24 + X

Solving for variable 'X'.

Reorder the terms:
4 + -24 + -1X + X2 = 24 + X + -24 + -1X

Combine like terms: 4 + -24 = -20
-20 + -1X + X2 = 24 + X + -24 + -1X

Reorder the terms:
-20 + -1X + X2 = 24 + -24 + X + -1X

Combine like terms: 24 + -24 = 0
-20 + -1X + X2 = 0 + X + -1X
-20 + -1X + X2 = X + -1X

Combine like terms: X + -1X = 0
-20 + -1X + X2 = 0

Factor a trinomial.
(-4 + -1X)(5 + -1X) = 0

Subproblem 1
Set the factor '(-4 + -1X)' equal to zero and attempt to solve:

Simplifying
-4 + -1X = 0

Solving
-4 + -1X = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1X = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1X = 0 + 4
-1X = 0 + 4

Combine like terms: 0 + 4 = 4
-1X = 4

Divide each side by '-1'.
X = -4

Simplifying
X = -4
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 = {-4, 5}