s(x-1)=s^2

Solution for s(x-1)=s^2 equation:

Simplifying
s(x + -1) = s2

Reorder the terms:
s(-1 + x) = s2
(-1 * s + x * s) = s2
(-1s + sx) = s2

Solving
-1s + sx = s2

Solving for variable 's'.

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

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

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 '(-1 + x + -1s)' equal to zero and attempt to solve:

Simplifying
-1 + x + -1s = 0

Reorder the terms:
-1 + -1s + x = 0

Solving
-1 + -1s + x = 0

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

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

Reorder the terms:
-1 + 1 + -1s + x = 0 + 1

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

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

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

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

Divide each side by '-1'.
s = -1 + x

Simplifying
s = -1 + x
Solution
s = {0, -1 + x}