x^2+17=7x+5

Solution for x^2+17=7x+5 equation:

Simplifying
x2 + 17 = 7x + 5

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

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

Solving
17 + x2 = 5 + 7x

Solving for variable 'x'.

Reorder the terms:
17 + -5 + -7x + x2 = 5 + 7x + -5 + -7x

Combine like terms: 17 + -5 = 12
12 + -7x + x2 = 5 + 7x + -5 + -7x

Reorder the terms:
12 + -7x + x2 = 5 + -5 + 7x + -7x

Combine like terms: 5 + -5 = 0
12 + -7x + x2 = 0 + 7x + -7x
12 + -7x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
12 + -7x + 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}