(7w+6r)(5w-11r)=

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Solution for (7w+6r)(5w-11r)= equation: 


Simplifying
(7w + 6r)(5w + -11r) = 0

Reorder the terms:
(6r + 7w)(5w + -11r) = 0

Reorder the terms:
(6r + 7w)(-11r + 5w) = 0

Multiply (6r + 7w) * (-11r + 5w)
(6r * (-11r + 5w) + 7w * (-11r + 5w)) = 0
((-11r * 6r + 5w * 6r) + 7w * (-11r + 5w)) = 0

Reorder the terms:
((30rw + -66r2) + 7w * (-11r + 5w)) = 0
((30rw + -66r2) + 7w * (-11r + 5w)) = 0
(30rw + -66r2 + (-11r * 7w + 5w * 7w)) = 0
(30rw + -66r2 + (-77rw + 35w2)) = 0

Reorder the terms:
(30rw + -77rw + -66r2 + 35w2) = 0

Combine like terms: 30rw + -77rw = -47rw
(-47rw + -66r2 + 35w2) = 0

Solving
-47rw + -66r2 + 35w2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-6r + -7w)(11r + -5w) = 0


Subproblem 1
Set the factor '(-6r + -7w)' equal to zero and attempt to solve:

Simplifying
-6r + -7w = 0

Solving
-6r + -7w = 0

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

Add '7w' to each side of the equation.
-6r + -7w + 7w = 0 + 7w

Combine like terms: -7w + 7w = 0
-6r + 0 = 0 + 7w
-6r = 0 + 7w
Remove the zero:
-6r = 7w

Divide each side by '-6'.
r = -1.166666667w

Simplifying
r = -1.166666667w

Subproblem 2
Set the factor '(11r + -5w)' equal to zero and attempt to solve:

Simplifying
11r + -5w = 0

Solving
11r + -5w = 0

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

Add '5w' to each side of the equation.
11r + -5w + 5w = 0 + 5w

Combine like terms: -5w + 5w = 0
11r + 0 = 0 + 5w
11r = 0 + 5w
Remove the zero:
11r = 5w

Divide each side by '11'.
r = 0.4545454545w

Simplifying
r = 0.4545454545w
Solution
r = {-1.166666667w, 0.4545454545w}

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