S(S-1)+7(S-1)=0

Solution for S(S-1)+7(S-1)=0 equation:

Simplifying
S(S + -1) + 7(S + -1) = 0

Reorder the terms:
S(-1 + S) + 7(S + -1) = 0
(-1 * S + S * S) + 7(S + -1) = 0
(-1S + S2) + 7(S + -1) = 0

Reorder the terms:
-1S + S2 + 7(-1 + S) = 0
-1S + S2 + (-1 * 7 + S * 7) = 0
-1S + S2 + (-7 + 7S) = 0

Reorder the terms:
-7 + -1S + 7S + S2 = 0

Combine like terms: -1S + 7S = 6S
-7 + 6S + S2 = 0

Solving
-7 + 6S + S2 = 0

Solving for variable 'S'.

Factor a trinomial.
(-7 + -1S)(1 + -1S) = 0

Subproblem 1
Set the factor '(-7 + -1S)' equal to zero and attempt to solve:

Simplifying
-7 + -1S = 0

Solving
-7 + -1S = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1S = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1S = 0 + 7
-1S = 0 + 7

Combine like terms: 0 + 7 = 7
-1S = 7

Divide each side by '-1'.
S = -7

Simplifying
S = -7
Subproblem 2
Set the factor '(1 + -1S)' equal to zero and attempt to solve:

Simplifying
1 + -1S = 0

Solving
1 + -1S = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1S = 0 + -1
-1S = 0 + -1

Combine like terms: 0 + -1 = -1
-1S = -1

Divide each side by '-1'.
S = 1

Simplifying
S = 1
Solution
S = {-7, 1}