x^2+1=5x+7

Solution for x^2+1=5x+7 equation:

Simplifying
x2 + 1 = 5x + 7

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

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

Solving
1 + x2 = 7 + 5x

Solving for variable 'x'.

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

Combine like terms: 1 + -7 = -6
-6 + -5x + x2 = 7 + 5x + -7 + -5x

Reorder the terms:
-6 + -5x + x2 = 7 + -7 + 5x + -5x

Combine like terms: 7 + -7 = 0
-6 + -5x + x2 = 0 + 5x + -5x
-6 + -5x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-6 + -5x + x2 = 0

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

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1
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 = {-1, 6}