x^2-7=x+5

Solution for x^2-7=x+5 equation:

Simplifying
x2 + -7 = x + 5

Reorder the terms:
-7 + x2 = x + 5

Reorder the terms:
-7 + x2 = 5 + x

Solving
-7 + x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
-7 + -5 + -1x + x2 = 5 + x + -5 + -1x

Combine like terms: -7 + -5 = -12
-12 + -1x + x2 = 5 + x + -5 + -1x

Reorder the terms:
-12 + -1x + x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
-12 + -1x + x2 = 0 + x + -1x
-12 + -1x + x2 = x + -1x

Combine like terms: x + -1x = 0
-12 + -1x + x2 = 0

Factor a trinomial.
(-3 + -1x)(4 + -1x) = 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 '(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
Solution
x = {-3, 4}