x^2+17x+22=8x+2

Solution for x^2+17x+22=8x+2 equation:

Simplifying
x2 + 17x + 22 = 8x + 2

Reorder the terms:
22 + 17x + x2 = 8x + 2

Reorder the terms:
22 + 17x + x2 = 2 + 8x

Solving
22 + 17x + x2 = 2 + 8x

Solving for variable 'x'.

Reorder the terms:
22 + -2 + 17x + -8x + x2 = 2 + 8x + -2 + -8x

Combine like terms: 22 + -2 = 20
20 + 17x + -8x + x2 = 2 + 8x + -2 + -8x

Combine like terms: 17x + -8x = 9x
20 + 9x + x2 = 2 + 8x + -2 + -8x

Reorder the terms:
20 + 9x + x2 = 2 + -2 + 8x + -8x

Combine like terms: 2 + -2 = 0
20 + 9x + x2 = 0 + 8x + -8x
20 + 9x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
20 + 9x + x2 = 0

Factor a trinomial.
(5 + x)(4 + x) = 0

Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {-5, -4}