(s-t)(7s+2t)=

Solution for (s-t)(7s+2t)= equation:

Simplifying
(s + -1t)(7s + 2t) = 0

Multiply (s + -1t) * (7s + 2t)
(s(7s + 2t) + -1t * (7s + 2t)) = 0
((7s * s + 2t * s) + -1t * (7s + 2t)) = 0

Reorder the terms:
((2st + 7s2) + -1t * (7s + 2t)) = 0
((2st + 7s2) + -1t * (7s + 2t)) = 0
(2st + 7s2 + (7s * -1t + 2t * -1t)) = 0
(2st + 7s2 + (-7st + -2t2)) = 0

Reorder the terms:
(2st + -7st + 7s2 + -2t2) = 0

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

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

Solving for variable 's'.

Factor a trinomial.
(s + -1t)(7s + 2t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7s + 2t)' equal to zero and attempt to solve:

Simplifying
7s + 2t = 0

Solving
7s + 2t = 0

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

Add '-2t' to each side of the equation.
7s + 2t + -2t = 0 + -2t

Combine like terms: 2t + -2t = 0
7s + 0 = 0 + -2t
7s = 0 + -2t
Remove the zero:
7s = -2t

Divide each side by '7'.
s = -0.2857142857t

Simplifying
s = -0.2857142857t
Solution
s = {t, -0.2857142857t}