(3t+5s)(5t-s)=

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Solution for (3t+5s)(5t-s)= equation: 


Simplifying
(3t + 5s)(5t + -1s) = 0

Reorder the terms:
(5s + 3t)(5t + -1s) = 0

Reorder the terms:
(5s + 3t)(-1s + 5t) = 0

Multiply (5s + 3t) * (-1s + 5t)
(5s * (-1s + 5t) + 3t * (-1s + 5t)) = 0
((-1s * 5s + 5t * 5s) + 3t * (-1s + 5t)) = 0

Reorder the terms:
((25st + -5s2) + 3t * (-1s + 5t)) = 0
((25st + -5s2) + 3t * (-1s + 5t)) = 0
(25st + -5s2 + (-1s * 3t + 5t * 3t)) = 0
(25st + -5s2 + (-3st + 15t2)) = 0

Reorder the terms:
(25st + -3st + -5s2 + 15t2) = 0

Combine like terms: 25st + -3st = 22st
(22st + -5s2 + 15t2) = 0

Solving
22st + -5s2 + 15t2 = 0

Solving for variable 's'.

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


Subproblem 1
Set the factor '(-5s + -3t)' equal to zero and attempt to solve:

Simplifying
-5s + -3t = 0

Solving
-5s + -3t = 0

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

Add '3t' to each side of the equation.
-5s + -3t + 3t = 0 + 3t

Combine like terms: -3t + 3t = 0
-5s + 0 = 0 + 3t
-5s = 0 + 3t
Remove the zero:
-5s = 3t

Divide each side by '-5'.
s = -0.6t

Simplifying
s = -0.6t

Subproblem 2
Set the factor '(s + -5t)' equal to zero and attempt to solve:

Simplifying
s + -5t = 0

Solving
s + -5t = 0

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

Add '5t' to each side of the equation.
s + -5t + 5t = 0 + 5t

Combine like terms: -5t + 5t = 0
s + 0 = 0 + 5t
s = 0 + 5t
Remove the zero:
s = 5t

Simplifying
s = 5t
Solution
s = {-0.6t, 5t}

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