(2S-4)(6-S)=0

Solution for (2S-4)(6-S)=0 equation:

Simplifying
(2S + -4)(6 + -1S) = 0

Reorder the terms:
(-4 + 2S)(6 + -1S) = 0

Multiply (-4 + 2S) * (6 + -1S)
(-4(6 + -1S) + 2S * (6 + -1S)) = 0
((6 * -4 + -1S * -4) + 2S * (6 + -1S)) = 0
((-24 + 4S) + 2S * (6 + -1S)) = 0
(-24 + 4S + (6 * 2S + -1S * 2S)) = 0
(-24 + 4S + (12S + -2S2)) = 0

Combine like terms: 4S + 12S = 16S
(-24 + 16S + -2S2) = 0

Solving
-24 + 16S + -2S2 = 0

Solving for variable 'S'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 8S + -1S2) = 0

Factor a trinomial.
2((-6 + S)(2 + -1S)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + S)' equal to zero and attempt to solve:

Simplifying
-6 + S = 0

Solving
-6 + S = 0

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

Add '6' to each side of the equation.
-6 + 6 + S = 0 + 6

Combine like terms: -6 + 6 = 0
0 + S = 0 + 6
S = 0 + 6

Combine like terms: 0 + 6 = 6
S = 6

Simplifying
S = 6
Subproblem 2
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
Solution
S = {6, 2}