s^2-3s-40=0

Solution for s^2-3s-40=0 equation:

Simplifying
s2 + -3s + -40 = 0

Reorder the terms:
-40 + -3s + s2 = 0

Solving
-40 + -3s + s2 = 0

Solving for variable 's'.

Factor a trinomial.
(-5 + -1s)(8 + -1s) = 0

Subproblem 1
Set the factor '(-5 + -1s)' equal to zero and attempt to solve:

Simplifying
-5 + -1s = 0

Solving
-5 + -1s = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1s = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1s = 0 + 5
-1s = 0 + 5

Combine like terms: 0 + 5 = 5
-1s = 5

Divide each side by '-1'.
s = -5

Simplifying
s = -5
Subproblem 2
Set the factor '(8 + -1s)' equal to zero and attempt to solve:

Simplifying
8 + -1s = 0

Solving
8 + -1s = 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 + -1s = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1s = 0 + -8
-1s = 0 + -8

Combine like terms: 0 + -8 = -8
-1s = -8

Divide each side by '-1'.
s = 8

Simplifying
s = 8
Solution
s = {-5, 8}