(3s+5)(2s-6)=0

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Solution for (3s+5)(2s-6)=0 equation:


Simplifying
(3s + 5)(2s + -6) = 0

Reorder the terms:
(5 + 3s)(2s + -6) = 0

Reorder the terms:
(5 + 3s)(-6 + 2s) = 0

Multiply (5 + 3s) * (-6 + 2s)
(5(-6 + 2s) + 3s * (-6 + 2s)) = 0
((-6 * 5 + 2s * 5) + 3s * (-6 + 2s)) = 0
((-30 + 10s) + 3s * (-6 + 2s)) = 0
(-30 + 10s + (-6 * 3s + 2s * 3s)) = 0
(-30 + 10s + (-18s + 6s2)) = 0

Combine like terms: 10s + -18s = -8s
(-30 + -8s + 6s2) = 0

Solving
-30 + -8s + 6s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -4s + 3s2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + -3s)' equal to zero and attempt to solve: Simplifying -5 + -3s = 0 Solving -5 + -3s = 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 + -3s = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3s = 0 + 5 -3s = 0 + 5 Combine like terms: 0 + 5 = 5 -3s = 5 Divide each side by '-3'. s = -1.666666667 Simplifying s = -1.666666667

Subproblem 2

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

Solution

s = {-1.666666667, 3}

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