(s+t)(5s-7t)=

Solution for (s+t)(5s-7t)= equation:

Simplifying
(s + t)(5s + -7t) = 0

Multiply (s + t) * (5s + -7t)
(s(5s + -7t) + t(5s + -7t)) = 0
((5s * s + -7t * s) + t(5s + -7t)) = 0

Reorder the terms:
((-7st + 5s2) + t(5s + -7t)) = 0
((-7st + 5s2) + t(5s + -7t)) = 0
(-7st + 5s2 + (5s * t + -7t * t)) = 0
(-7st + 5s2 + (5st + -7t2)) = 0

Reorder the terms:
(-7st + 5st + 5s2 + -7t2) = 0

Combine like terms: -7st + 5st = -2st
(-2st + 5s2 + -7t2) = 0

Solving
-2st + 5s2 + -7t2 = 0

Solving for variable 's'.

Factor a trinomial.
(5s + -7t)(s + t) = 0

Subproblem 1
Set the factor '(5s + -7t)' equal to zero and attempt to solve:

Simplifying
5s + -7t = 0

Solving
5s + -7t = 0

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

Add '7t' to each side of the equation.
5s + -7t + 7t = 0 + 7t

Combine like terms: -7t + 7t = 0
5s + 0 = 0 + 7t
5s = 0 + 7t
Remove the zero:
5s = 7t

Divide each side by '5'.
s = 1.4t

Simplifying
s = 1.4t
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 = {1.4t, -1t}