x^2+10x+17=-7

Solution for x^2+10x+17=-7 equation:

Simplifying
x2 + 10x + 17 = -7

Reorder the terms:
17 + 10x + x2 = -7

Solving
17 + 10x + x2 = -7

Solving for variable 'x'.

Reorder the terms:
17 + 7 + 10x + x2 = -7 + 7

Combine like terms: 17 + 7 = 24
24 + 10x + x2 = -7 + 7

Combine like terms: -7 + 7 = 0
24 + 10x + x2 = 0

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

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
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 = {-6, -4}