s^2-2s=3s+24

Solution for s^2-2s=3s+24 equation:

Simplifying
s2 + -2s = 3s + 24

Reorder the terms:
-2s + s2 = 3s + 24

Reorder the terms:
-2s + s2 = 24 + 3s

Solving
-2s + s2 = 24 + 3s

Solving for variable 's'.

Reorder the terms:
-24 + -2s + -3s + s2 = 24 + 3s + -24 + -3s

Combine like terms: -2s + -3s = -5s
-24 + -5s + s2 = 24 + 3s + -24 + -3s

Reorder the terms:
-24 + -5s + s2 = 24 + -24 + 3s + -3s

Combine like terms: 24 + -24 = 0
-24 + -5s + s2 = 0 + 3s + -3s
-24 + -5s + s2 = 3s + -3s

Combine like terms: 3s + -3s = 0
-24 + -5s + s2 = 0

Factor a trinomial.
(-3 + -1s)(8 + -1s) = 0

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

Simplifying
-3 + -1s = 0

Solving
-3 + -1s = 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 + -1s = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1s = 0 + 3
-1s = 0 + 3

Combine like terms: 0 + 3 = 3
-1s = 3

Divide each side by '-1'.
s = -3

Simplifying
s = -3
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 = {-3, 8}