(11t-s)(t+5s)=

Solution for (11t-s)(t+5s)= equation:

Simplifying
(11t + -1s)(t + 5s) = 0

Reorder the terms:
(-1s + 11t)(t + 5s) = 0

Reorder the terms:
(-1s + 11t)(5s + t) = 0

Multiply (-1s + 11t) * (5s + t)
(-1s * (5s + t) + 11t * (5s + t)) = 0
((5s * -1s + t * -1s) + 11t * (5s + t)) = 0

Reorder the terms:
((-1st + -5s2) + 11t * (5s + t)) = 0
((-1st + -5s2) + 11t * (5s + t)) = 0
(-1st + -5s2 + (5s * 11t + t * 11t)) = 0
(-1st + -5s2 + (55st + 11t2)) = 0

Reorder the terms:
(-1st + 55st + -5s2 + 11t2) = 0

Combine like terms: -1st + 55st = 54st
(54st + -5s2 + 11t2) = 0

Solving
54st + -5s2 + 11t2 = 0

Solving for variable 's'.

Factor a trinomial.
(-5s + -1t)(s + -11t) = 0

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

Simplifying
-5s + -1t = 0

Solving
-5s + -1t = 0

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

Add 't' to each side of the equation.
-5s + -1t + t = 0 + t

Combine like terms: -1t + t = 0
-5s + 0 = 0 + t
-5s = 0 + t
Remove the zero:
-5s = t

Divide each side by '-5'.
s = -0.2t

Simplifying
s = -0.2t
Subproblem 2
Set the factor '(s + -11t)' equal to zero and attempt to solve:

Simplifying
s + -11t = 0

Solving
s + -11t = 0

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

Add '11t' to each side of the equation.
s + -11t + 11t = 0 + 11t

Combine like terms: -11t + 11t = 0
s + 0 = 0 + 11t
s = 0 + 11t
Remove the zero:
s = 11t

Simplifying
s = 11t
Solution
s = {-0.2t, 11t}