s^2-5s=2s+18

Solution for s^2-5s=2s+18 equation:

Simplifying
s2 + -5s = 2s + 18

Reorder the terms:
-5s + s2 = 2s + 18

Reorder the terms:
-5s + s2 = 18 + 2s

Solving
-5s + s2 = 18 + 2s

Solving for variable 's'.

Reorder the terms:
-18 + -5s + -2s + s2 = 18 + 2s + -18 + -2s

Combine like terms: -5s + -2s = -7s
-18 + -7s + s2 = 18 + 2s + -18 + -2s

Reorder the terms:
-18 + -7s + s2 = 18 + -18 + 2s + -2s

Combine like terms: 18 + -18 = 0
-18 + -7s + s2 = 0 + 2s + -2s
-18 + -7s + s2 = 2s + -2s

Combine like terms: 2s + -2s = 0
-18 + -7s + s2 = 0

Factor a trinomial.
(-2 + -1s)(9 + -1s) = 0

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

Simplifying
-2 + -1s = 0

Solving
-2 + -1s = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1s = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1s = 0 + 2
-1s = 0 + 2

Combine like terms: 0 + 2 = 2
-1s = 2

Divide each side by '-1'.
s = -2

Simplifying
s = -2
Subproblem 2
Set the factor '(9 + -1s)' equal to zero and attempt to solve:

Simplifying
9 + -1s = 0

Solving
9 + -1s = 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 + -1s = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1s = 0 + -9
-1s = 0 + -9

Combine like terms: 0 + -9 = -9
-1s = -9

Divide each side by '-1'.
s = 9

Simplifying
s = 9
Solution
s = {-2, 9}