20w^2+17wr-63r^2=

Solution for 20w^2+17wr-63r^2= equation:

Simplifying
20w2 + 17wr + -63r2 = 0

Reorder the terms:
17rw + -63r2 + 20w2 = 0

Solving
17rw + -63r2 + 20w2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-9r + -4w)(7r + -5w) = 0

Subproblem 1
Set the factor '(-9r + -4w)' equal to zero and attempt to solve:

Simplifying
-9r + -4w = 0

Solving
-9r + -4w = 0

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

Add '4w' to each side of the equation.
-9r + -4w + 4w = 0 + 4w

Combine like terms: -4w + 4w = 0
-9r + 0 = 0 + 4w
-9r = 0 + 4w
Remove the zero:
-9r = 4w

Divide each side by '-9'.
r = -0.4444444444w

Simplifying
r = -0.4444444444w
Subproblem 2
Set the factor '(7r + -5w)' equal to zero and attempt to solve:

Simplifying
7r + -5w = 0

Solving
7r + -5w = 0

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

Add '5w' to each side of the equation.
7r + -5w + 5w = 0 + 5w

Combine like terms: -5w + 5w = 0
7r + 0 = 0 + 5w
7r = 0 + 5w
Remove the zero:
7r = 5w

Divide each side by '7'.
r = 0.7142857143w

Simplifying
r = 0.7142857143w
Solution
r = {-0.4444444444w, 0.7142857143w}