(X^2+6)=(36+X)

Solution for (X^2+6)=(36+X) equation:

Simplifying
(X2 + 6) = (36 + X)

Reorder the terms:
(6 + X2) = (36 + X)

Remove parenthesis around (6 + X2)
6 + X2 = (36 + X)

Remove parenthesis around (36 + X)
6 + X2 = 36 + X

Solving
6 + X2 = 36 + X

Solving for variable 'X'.

Reorder the terms:
6 + -36 + -1X + X2 = 36 + X + -36 + -1X

Combine like terms: 6 + -36 = -30
-30 + -1X + X2 = 36 + X + -36 + -1X

Reorder the terms:
-30 + -1X + X2 = 36 + -36 + X + -1X

Combine like terms: 36 + -36 = 0
-30 + -1X + X2 = 0 + X + -1X
-30 + -1X + X2 = X + -1X

Combine like terms: X + -1X = 0
-30 + -1X + X2 = 0

Factor a trinomial.
(-5 + -1X)(6 + -1X) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1X)' equal to zero and attempt to solve:

Simplifying
6 + -1X = 0

Solving
6 + -1X = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1X = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1X = 0 + -6
-1X = 0 + -6

Combine like terms: 0 + -6 = -6
-1X = -6

Divide each side by '-1'.
X = 6

Simplifying
X = 6
Solution
X = {-5, 6}