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

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

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

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

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

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

Reorder the terms:
(3st + -1st + -3s2 + t2) = 0

Combine like terms: 3st + -1st = 2st
(2st + -3s2 + t2) = 0

Solving
2st + -3s2 + t2 = 0

Solving for variable 's'.

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

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

Simplifying
-3s + -1t = 0

Solving
-3s + -1t = 0

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

Add 't' to each side of the equation.
-3s + -1t + t = 0 + t

Combine like terms: -1t + t = 0
-3s + 0 = 0 + t
-3s = 0 + t
Remove the zero:
-3s = t

Divide each side by '-3'.
s = -0.3333333333t

Simplifying
s = -0.3333333333t
Subproblem 2
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
Solution
s = {-0.3333333333t, t}