s^2-6s=2s+20

Solution for s^2-6s=2s+20 equation:

Simplifying
s2 + -6s = 2s + 20

Reorder the terms:
-6s + s2 = 2s + 20

Reorder the terms:
-6s + s2 = 20 + 2s

Solving
-6s + s2 = 20 + 2s

Solving for variable 's'.

Reorder the terms:
-20 + -6s + -2s + s2 = 20 + 2s + -20 + -2s

Combine like terms: -6s + -2s = -8s
-20 + -8s + s2 = 20 + 2s + -20 + -2s

Reorder the terms:
-20 + -8s + s2 = 20 + -20 + 2s + -2s

Combine like terms: 20 + -20 = 0
-20 + -8s + s2 = 0 + 2s + -2s
-20 + -8s + s2 = 2s + -2s

Combine like terms: 2s + -2s = 0
-20 + -8s + s2 = 0

Factor a trinomial.
(-2 + -1s)(10 + -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 '(10 + -1s)' equal to zero and attempt to solve:

Simplifying
10 + -1s = 0

Solving
10 + -1s = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1s = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1s = 0 + -10
-1s = 0 + -10

Combine like terms: 0 + -10 = -10
-1s = -10

Divide each side by '-1'.
s = 10

Simplifying
s = 10
Solution
s = {-2, 10}