(s-1)(s-5)=32

Solution for (s-1)(s-5)=32 equation:

Simplifying
(s + -1)(s + -5) = 32

Reorder the terms:
(-1 + s)(s + -5) = 32

Reorder the terms:
(-1 + s)(-5 + s) = 32

Multiply (-1 + s) * (-5 + s)
(-1(-5 + s) + s(-5 + s)) = 32
((-5 * -1 + s * -1) + s(-5 + s)) = 32
((5 + -1s) + s(-5 + s)) = 32
(5 + -1s + (-5 * s + s * s)) = 32
(5 + -1s + (-5s + s2)) = 32

Combine like terms: -1s + -5s = -6s
(5 + -6s + s2) = 32

Solving
5 + -6s + s2 = 32

Solving for variable 's'.

Reorder the terms:
5 + -32 + -6s + s2 = 32 + -32

Combine like terms: 5 + -32 = -27
-27 + -6s + s2 = 32 + -32

Combine like terms: 32 + -32 = 0
-27 + -6s + s2 = 0

Factor a trinomial.
(-3 + -1s)(9 + -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 '(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 = {-3, 9}