5s(6s-5)(5s-1)=0

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Solution for 5s(6s-5)(5s-1)=0 equation:


Simplifying
5s(6s + -5)(5s + -1) = 0

Reorder the terms:
5s(-5 + 6s)(5s + -1) = 0

Reorder the terms:
5s(-5 + 6s)(-1 + 5s) = 0

Multiply (-5 + 6s) * (-1 + 5s)
5s(-5(-1 + 5s) + 6s * (-1 + 5s)) = 0
5s((-1 * -5 + 5s * -5) + 6s * (-1 + 5s)) = 0
5s((5 + -25s) + 6s * (-1 + 5s)) = 0
5s(5 + -25s + (-1 * 6s + 5s * 6s)) = 0
5s(5 + -25s + (-6s + 30s2)) = 0

Combine like terms: -25s + -6s = -31s
5s(5 + -31s + 30s2) = 0
(5 * 5s + -31s * 5s + 30s2 * 5s) = 0
(25s + -155s2 + 150s3) = 0

Solving
25s + -155s2 + 150s3 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '5s'.
5s(5 + -31s + 30s2) = 0

Factor a trinomial.
5s((1 + -5s)(5 + -6s)) = 0

Ignore the factor 5.

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 '(1 + -5s)' equal to zero and attempt to solve: Simplifying 1 + -5s = 0 Solving 1 + -5s = 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 + -5s = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5s = 0 + -1 -5s = 0 + -1 Combine like terms: 0 + -1 = -1 -5s = -1 Divide each side by '-5'. s = 0.2 Simplifying s = 0.2

Subproblem 3

Set the factor '(5 + -6s)' equal to zero and attempt to solve: Simplifying 5 + -6s = 0 Solving 5 + -6s = 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 + -6s = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6s = 0 + -5 -6s = 0 + -5 Combine like terms: 0 + -5 = -5 -6s = -5 Divide each side by '-6'. s = 0.8333333333 Simplifying s = 0.8333333333

Solution

s = {0, 0.2, 0.8333333333}

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