s^2+10s+21=0

Solution for s^2+10s+21=0 equation:

Simplifying
s2 + 10s + 21 = 0

Reorder the terms:
21 + 10s + s2 = 0

Solving
21 + 10s + s2 = 0

Solving for variable 's'.

Factor a trinomial.
(7 + s)(3 + s) = 0

Subproblem 1
Set the factor '(7 + s)' equal to zero and attempt to solve:

Simplifying
7 + s = 0

Solving
7 + s = 0

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

Add '-7' to each side of the equation.
7 + -7 + s = 0 + -7

Combine like terms: 7 + -7 = 0
0 + s = 0 + -7
s = 0 + -7

Combine like terms: 0 + -7 = -7
s = -7

Simplifying
s = -7
Subproblem 2
Set the factor '(3 + s)' equal to zero and attempt to solve:

Simplifying
3 + s = 0

Solving
3 + s = 0

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

Add '-3' to each side of the equation.
3 + -3 + s = 0 + -3

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

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

Simplifying
s = -3
Solution
s = {-7, -3}