(6s+3ya)(s+ya)=0

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Solution for (6s+3ya)(s+ya)=0 equation:


Simplifying
(6s + 3ya)(s + ya) = 0

Reorder the terms:
(3ay + 6s)(s + ya) = 0

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

Multiply (3ay + 6s) * (ay + s)
(3ay * (ay + s) + 6s * (ay + s)) = 0
((ay * 3ay + s * 3ay) + 6s * (ay + s)) = 0

Reorder the terms:
((3asy + 3a2y2) + 6s * (ay + s)) = 0
((3asy + 3a2y2) + 6s * (ay + s)) = 0
(3asy + 3a2y2 + (ay * 6s + s * 6s)) = 0
(3asy + 3a2y2 + (6asy + 6s2)) = 0

Reorder the terms:
(3asy + 6asy + 3a2y2 + 6s2) = 0

Combine like terms: 3asy + 6asy = 9asy
(9asy + 3a2y2 + 6s2) = 0

Solving
9asy + 3a2y2 + 6s2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3asy + a2y2 + 2s2) = 0

Factor a trinomial.
3((ay + s)(ay + 2s)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(ay + s)' equal to zero and attempt to solve: Simplifying ay + s = 0 Solving ay + s = 0 Move all terms containing a to the left, all other terms to the right. Add '-1s' to each side of the equation. ay + s + -1s = 0 + -1s Combine like terms: s + -1s = 0 ay + 0 = 0 + -1s ay = 0 + -1s Remove the zero: ay = -1s Divide each side by 'y'. a = -1sy-1 Simplifying a = -1sy-1

Subproblem 2

Set the factor '(ay + 2s)' equal to zero and attempt to solve: Simplifying ay + 2s = 0 Solving ay + 2s = 0 Move all terms containing a to the left, all other terms to the right. Add '-2s' to each side of the equation. ay + 2s + -2s = 0 + -2s Combine like terms: 2s + -2s = 0 ay + 0 = 0 + -2s ay = 0 + -2s Remove the zero: ay = -2s Divide each side by 'y'. a = -2sy-1 Simplifying a = -2sy-1

Solution

a = {-1sy-1, -2sy-1}

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