(s-t)(3s+8t)=0

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Solution for (s-t)(3s+8t)=0 equation: 


Simplifying
(s + -1t)(3s + 8t) = 0

Multiply (s + -1t) * (3s + 8t)
(s(3s + 8t) + -1t * (3s + 8t)) = 0
((3s * s + 8t * s) + -1t * (3s + 8t)) = 0

Reorder the terms:
((8st + 3s2) + -1t * (3s + 8t)) = 0
((8st + 3s2) + -1t * (3s + 8t)) = 0
(8st + 3s2 + (3s * -1t + 8t * -1t)) = 0
(8st + 3s2 + (-3st + -8t2)) = 0

Reorder the terms:
(8st + -3st + 3s2 + -8t2) = 0

Combine like terms: 8st + -3st = 5st
(5st + 3s2 + -8t2) = 0

Solving
5st + 3s2 + -8t2 = 0

Solving for variable 's'.

Factor a trinomial.
(s + -1t)(3s + 8t) = 0


Subproblem 1
Set the factor '(s + -1t)' equal to zero and attempt to solve:

Simplifying
s + -1t = 0

Solving
s + -1t = 0

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

Add 't' to each side of the equation.
s + -1t + t = 0 + t

Combine like terms: -1t + t = 0
s + 0 = 0 + t
s = 0 + t
Remove the zero:
s = t

Simplifying
s = t

Subproblem 2
Set the factor '(3s + 8t)' equal to zero and attempt to solve:

Simplifying
3s + 8t = 0

Solving
3s + 8t = 0

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

Add '-8t' to each side of the equation.
3s + 8t + -8t = 0 + -8t

Combine like terms: 8t + -8t = 0
3s + 0 = 0 + -8t
3s = 0 + -8t
Remove the zero:
3s = -8t

Divide each side by '3'.
s = -2.666666667t

Simplifying
s = -2.666666667t
Solution
s = {t, -2.666666667t}

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