s(3s-6)(s-4)=0

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Solution for s(3s-6)(s-4)=0 equation:


Simplifying
s(3s + -6)(s + -4) = 0

Reorder the terms:
s(-6 + 3s)(s + -4) = 0

Reorder the terms:
s(-6 + 3s)(-4 + s) = 0

Multiply (-6 + 3s) * (-4 + s)
s(-6(-4 + s) + 3s * (-4 + s)) = 0
s((-4 * -6 + s * -6) + 3s * (-4 + s)) = 0
s((24 + -6s) + 3s * (-4 + s)) = 0
s(24 + -6s + (-4 * 3s + s * 3s)) = 0
s(24 + -6s + (-12s + 3s2)) = 0

Combine like terms: -6s + -12s = -18s
s(24 + -18s + 3s2) = 0
(24 * s + -18s * s + 3s2 * s) = 0
(24s + -18s2 + 3s3) = 0

Solving
24s + -18s2 + 3s3 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '3s'.
3s(8 + -6s + s2) = 0

Factor a trinomial.
3s((2 + -1s)(4 + -1s)) = 0

Ignore the factor 3.

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 '(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

Subproblem 3

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 = {0, 2, 4}

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