x^2+6=5x+2

Solution for x^2+6=5x+2 equation:

Simplifying
x2 + 6 = 5x + 2

Reorder the terms:
6 + x2 = 5x + 2

Reorder the terms:
6 + x2 = 2 + 5x

Solving
6 + x2 = 2 + 5x

Solving for variable 'x'.

Reorder the terms:
6 + -2 + -5x + x2 = 2 + 5x + -2 + -5x

Combine like terms: 6 + -2 = 4
4 + -5x + x2 = 2 + 5x + -2 + -5x

Reorder the terms:
4 + -5x + x2 = 2 + -2 + 5x + -5x

Combine like terms: 2 + -2 = 0
4 + -5x + x2 = 0 + 5x + -5x
4 + -5x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
4 + -5x + x2 = 0

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