x^2+7x+10=-2

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

Simplifying
x2 + 7x + 10 = -2

Reorder the terms:
10 + 7x + x2 = -2

Solving
10 + 7x + x2 = -2

Solving for variable 'x'.

Reorder the terms:
10 + 2 + 7x + x2 = -2 + 2

Combine like terms: 10 + 2 = 12
12 + 7x + x2 = -2 + 2

Combine like terms: -2 + 2 = 0
12 + 7x + x2 = 0

Factor a trinomial.
(4 + x)(3 + x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-4, -3}