(2s+t)(5s-3t)=

Solution for (2s+t)(5s-3t)= equation:

Simplifying
(2s + t)(5s + -3t) = 0

Multiply (2s + t) * (5s + -3t)
(2s * (5s + -3t) + t(5s + -3t)) = 0
((5s * 2s + -3t * 2s) + t(5s + -3t)) = 0

Reorder the terms:
((-6st + 10s2) + t(5s + -3t)) = 0
((-6st + 10s2) + t(5s + -3t)) = 0
(-6st + 10s2 + (5s * t + -3t * t)) = 0
(-6st + 10s2 + (5st + -3t2)) = 0

Reorder the terms:
(-6st + 5st + 10s2 + -3t2) = 0

Combine like terms: -6st + 5st = -1st
(-1st + 10s2 + -3t2) = 0

Solving
-1st + 10s2 + -3t2 = 0

Solving for variable 's'.

Factor a trinomial.
(5s + -3t)(2s + t) = 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 '(2s + t)' equal to zero and attempt to solve:

Simplifying
2s + t = 0

Solving
2s + t = 0

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

Add '-1t' to each side of the equation.
2s + t + -1t = 0 + -1t

Combine like terms: t + -1t = 0
2s + 0 = 0 + -1t
2s = 0 + -1t
Remove the zero:
2s = -1t

Divide each side by '2'.
s = -0.5t

Simplifying
s = -0.5t
Solution
s = {0.6t, -0.5t}