S^2=7S-12

Solution for S^2=7S-12 equation:

Simplifying
S2 = 7S + -12

Reorder the terms:
S2 = -12 + 7S

Solving
S2 = -12 + 7S

Solving for variable 'S'.

Reorder the terms:
12 + -7S + S2 = -12 + 7S + 12 + -7S

Reorder the terms:
12 + -7S + S2 = -12 + 12 + 7S + -7S

Combine like terms: -12 + 12 = 0
12 + -7S + S2 = 0 + 7S + -7S
12 + -7S + S2 = 7S + -7S

Combine like terms: 7S + -7S = 0
12 + -7S + S2 = 0

Factor a trinomial.
(3 + -1S)(4 + -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 '(4 + -1S)' equal to zero and attempt to solve:

Simplifying
4 + -1S = 0

Solving
4 + -1S = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1S = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1S = 0 + -4
-1S = 0 + -4

Combine like terms: 0 + -4 = -4
-1S = -4

Divide each side by '-1'.
S = 4

Simplifying
S = 4
Solution
S = {3, 4}