3-13s=3-8s+s^2

Solution for 3-13s=3-8s+s^2 equation:

Simplifying
3 + -13s = 3 + -8s + s2

Add '-3' to each side of the equation.
3 + -3 + -13s = 3 + -8s + -3 + s2

Combine like terms: 3 + -3 = 0
0 + -13s = 3 + -8s + -3 + s2
-13s = 3 + -8s + -3 + s2

Reorder the terms:
-13s = 3 + -3 + -8s + s2

Combine like terms: 3 + -3 = 0
-13s = 0 + -8s + s2
-13s = -8s + s2

Solving
-13s = -8s + s2

Solving for variable 's'.

Combine like terms: -13s + 8s = -5s
-5s + -1s2 = -8s + s2 + 8s + -1s2

Reorder the terms:
-5s + -1s2 = -8s + 8s + s2 + -1s2

Combine like terms: -8s + 8s = 0
-5s + -1s2 = 0 + s2 + -1s2
-5s + -1s2 = s2 + -1s2

Combine like terms: s2 + -1s2 = 0
-5s + -1s2 = 0

Factor out the Greatest Common Factor (GCF), '-1s'.
-1s(5 + s) = 0

Ignore the factor -1.
Subproblem 1
Set the factor 's' equal to zero and attempt to solve:

Simplifying
s = 0

Solving
s = 0

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

Simplifying
s = 0
Subproblem 2
Set the factor '(5 + s)' equal to zero and attempt to solve:

Simplifying
5 + s = 0

Solving
5 + s = 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 + s = 0 + -5

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

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

Simplifying
s = -5
Solution
s = {0, -5}