(2s-4)(2s-3)=2s^2+2(s-9)

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Solution for (2s-4)(2s-3)=2s^2+2(s-9) equation: 


Simplifying
(2s + -4)(2s + -3) = 2s2 + 2(s + -9)

Reorder the terms:
(-4 + 2s)(2s + -3) = 2s2 + 2(s + -9)

Reorder the terms:
(-4 + 2s)(-3 + 2s) = 2s2 + 2(s + -9)

Multiply (-4 + 2s) * (-3 + 2s)
(-4(-3 + 2s) + 2s * (-3 + 2s)) = 2s2 + 2(s + -9)
((-3 * -4 + 2s * -4) + 2s * (-3 + 2s)) = 2s2 + 2(s + -9)
((12 + -8s) + 2s * (-3 + 2s)) = 2s2 + 2(s + -9)
(12 + -8s + (-3 * 2s + 2s * 2s)) = 2s2 + 2(s + -9)
(12 + -8s + (-6s + 4s2)) = 2s2 + 2(s + -9)

Combine like terms: -8s + -6s = -14s
(12 + -14s + 4s2) = 2s2 + 2(s + -9)

Reorder the terms:
12 + -14s + 4s2 = 2s2 + 2(-9 + s)
12 + -14s + 4s2 = 2s2 + (-9 * 2 + s * 2)
12 + -14s + 4s2 = 2s2 + (-18 + 2s)

Reorder the terms:
12 + -14s + 4s2 = -18 + 2s + 2s2

Solving
12 + -14s + 4s2 = -18 + 2s + 2s2

Solving for variable 's'.

Reorder the terms:
12 + 18 + -14s + -2s + 4s2 + -2s2 = -18 + 2s + 2s2 + 18 + -2s + -2s2

Combine like terms: 12 + 18 = 30
30 + -14s + -2s + 4s2 + -2s2 = -18 + 2s + 2s2 + 18 + -2s + -2s2

Combine like terms: -14s + -2s = -16s
30 + -16s + 4s2 + -2s2 = -18 + 2s + 2s2 + 18 + -2s + -2s2

Combine like terms: 4s2 + -2s2 = 2s2
30 + -16s + 2s2 = -18 + 2s + 2s2 + 18 + -2s + -2s2

Reorder the terms:
30 + -16s + 2s2 = -18 + 18 + 2s + -2s + 2s2 + -2s2

Combine like terms: -18 + 18 = 0
30 + -16s + 2s2 = 0 + 2s + -2s + 2s2 + -2s2
30 + -16s + 2s2 = 2s + -2s + 2s2 + -2s2

Combine like terms: 2s + -2s = 0
30 + -16s + 2s2 = 0 + 2s2 + -2s2
30 + -16s + 2s2 = 2s2 + -2s2

Combine like terms: 2s2 + -2s2 = 0
30 + -16s + 2s2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -8s + s2) = 0

Factor a trinomial.
2((3 + -1s)(5 + -1s)) = 0

Ignore the factor 2.

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 '(5 + -1s)' equal to zero and attempt to solve:

Simplifying
5 + -1s = 0

Solving
5 + -1s = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1s = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1s = 0 + -5
-1s = 0 + -5

Combine like terms: 0 + -5 = -5
-1s = -5

Divide each side by '-1'.
s = 5

Simplifying
s = 5
Solution
s = {3, 5}

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