S^2+17S+72=0

Solution for S^2+17S+72=0 equation:

Simplifying
S2 + 17S + 72 = 0

Reorder the terms:
72 + 17S + S2 = 0

Solving
72 + 17S + S2 = 0

Solving for variable 'S'.

Factor a trinomial.
(9 + S)(8 + S) = 0

Subproblem 1
Set the factor '(9 + S)' equal to zero and attempt to solve:

Simplifying
9 + S = 0

Solving
9 + S = 0

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

Add '-9' to each side of the equation.
9 + -9 + S = 0 + -9

Combine like terms: 9 + -9 = 0
0 + S = 0 + -9
S = 0 + -9

Combine like terms: 0 + -9 = -9
S = -9

Simplifying
S = -9
Subproblem 2
Set the factor '(8 + S)' equal to zero and attempt to solve:

Simplifying
8 + S = 0

Solving
8 + S = 0

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

Add '-8' to each side of the equation.
8 + -8 + S = 0 + -8

Combine like terms: 8 + -8 = 0
0 + S = 0 + -8
S = 0 + -8

Combine like terms: 0 + -8 = -8
S = -8

Simplifying
S = -8
Solution
S = {-9, -8}