x^2+13x+22=10

Solution for x^2+13x+22=10 equation:

Simplifying
x2 + 13x + 22 = 10

Reorder the terms:
22 + 13x + x2 = 10

Solving
22 + 13x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
22 + -10 + 13x + x2 = 10 + -10

Combine like terms: 22 + -10 = 12
12 + 13x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
12 + 13x + x2 = 0

Factor a trinomial.
(12 + x)(1 + x) = 0

Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

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

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

Simplifying
x = -12
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-12, -1}