(11s+r)(-7r+s)=

Solution for (11s+r)(-7r+s)= equation:

Simplifying
(11s + r)(-7r + s) = 0

Reorder the terms:
(r + 11s)(-7r + s) = 0

Multiply (r + 11s) * (-7r + s)
(r(-7r + s) + 11s * (-7r + s)) = 0
((-7r * r + s * r) + 11s * (-7r + s)) = 0

Reorder the terms:
((rs + -7r2) + 11s * (-7r + s)) = 0
((rs + -7r2) + 11s * (-7r + s)) = 0
(rs + -7r2 + (-7r * 11s + s * 11s)) = 0
(rs + -7r2 + (-77rs + 11s2)) = 0

Reorder the terms:
(rs + -77rs + -7r2 + 11s2) = 0

Combine like terms: rs + -77rs = -76rs
(-76rs + -7r2 + 11s2) = 0

Solving
-76rs + -7r2 + 11s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1r + -11s)(7r + -1s) = 0

Subproblem 1
Set the factor '(-1r + -11s)' equal to zero and attempt to solve:

Simplifying
-1r + -11s = 0

Solving
-1r + -11s = 0

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

Add '11s' to each side of the equation.
-1r + -11s + 11s = 0 + 11s

Combine like terms: -11s + 11s = 0
-1r + 0 = 0 + 11s
-1r = 0 + 11s
Remove the zero:
-1r = 11s

Divide each side by '-1'.
r = -11s

Simplifying
r = -11s
Subproblem 2
Set the factor '(7r + -1s)' equal to zero and attempt to solve:

Simplifying
7r + -1s = 0

Solving
7r + -1s = 0

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

Add 's' to each side of the equation.
7r + -1s + s = 0 + s

Combine like terms: -1s + s = 0
7r + 0 = 0 + s
7r = 0 + s
Remove the zero:
7r = s

Divide each side by '7'.
r = 0.1428571429s

Simplifying
r = 0.1428571429s
Solution
r = {-11s, 0.1428571429s}