(s+t)(3s-4t)=0

Solution for (s+t)(3s-4t)=0 equation:

Simplifying
(s + t)(3s + -4t) = 0

Multiply (s + t) * (3s + -4t)
(s(3s + -4t) + t(3s + -4t)) = 0
((3s * s + -4t * s) + t(3s + -4t)) = 0

Reorder the terms:
((-4st + 3s2) + t(3s + -4t)) = 0
((-4st + 3s2) + t(3s + -4t)) = 0
(-4st + 3s2 + (3s * t + -4t * t)) = 0
(-4st + 3s2 + (3st + -4t2)) = 0

Reorder the terms:
(-4st + 3st + 3s2 + -4t2) = 0

Combine like terms: -4st + 3st = -1st
(-1st + 3s2 + -4t2) = 0

Solving
-1st + 3s2 + -4t2 = 0

Solving for variable 's'.

Factor a trinomial.
(3s + -4t)(s + t) = 0

Subproblem 1
Set the factor '(3s + -4t)' equal to zero and attempt to solve:

Simplifying
3s + -4t = 0

Solving
3s + -4t = 0

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

Add '4t' to each side of the equation.
3s + -4t + 4t = 0 + 4t

Combine like terms: -4t + 4t = 0
3s + 0 = 0 + 4t
3s = 0 + 4t
Remove the zero:
3s = 4t

Divide each side by '3'.
s = 1.333333333t

Simplifying
s = 1.333333333t
Subproblem 2
Set the factor '(s + t)' equal to zero and attempt to solve:

Simplifying
s + t = 0

Solving
s + t = 0

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

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

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

Simplifying
s = -1t
Solution
s = {1.333333333t, -1t}