s^2=5s-6

Solution for s^2=5s-6 equation:

Simplifying
s2 = 5s + -6

Reorder the terms:
s2 = -6 + 5s

Solving
s2 = -6 + 5s

Solving for variable 's'.

Reorder the terms:
6 + -5s + s2 = -6 + 5s + 6 + -5s

Reorder the terms:
6 + -5s + s2 = -6 + 6 + 5s + -5s

Combine like terms: -6 + 6 = 0
6 + -5s + s2 = 0 + 5s + -5s
6 + -5s + s2 = 5s + -5s

Combine like terms: 5s + -5s = 0
6 + -5s + s2 = 0

Factor a trinomial.
(2 + -1s)(3 + -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 '(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
Solution
s = {2, 3}