12w^2+13wr-35r^2=

Solution for 12w^2+13wr-35r^2= equation:

Simplifying
12w2 + 13wr + -35r2 = 0

Reorder the terms:
13rw + -35r2 + 12w2 = 0

Solving
13rw + -35r2 + 12w2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-7r + -3w)(5r + -4w) = 0

Subproblem 1
Set the factor '(-7r + -3w)' equal to zero and attempt to solve:

Simplifying
-7r + -3w = 0

Solving
-7r + -3w = 0

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

Add '3w' to each side of the equation.
-7r + -3w + 3w = 0 + 3w

Combine like terms: -3w + 3w = 0
-7r + 0 = 0 + 3w
-7r = 0 + 3w
Remove the zero:
-7r = 3w

Divide each side by '-7'.
r = -0.4285714286w

Simplifying
r = -0.4285714286w
Subproblem 2
Set the factor '(5r + -4w)' equal to zero and attempt to solve:

Simplifying
5r + -4w = 0

Solving
5r + -4w = 0

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

Add '4w' to each side of the equation.
5r + -4w + 4w = 0 + 4w

Combine like terms: -4w + 4w = 0
5r + 0 = 0 + 4w
5r = 0 + 4w
Remove the zero:
5r = 4w

Divide each side by '5'.
r = 0.8w

Simplifying
r = 0.8w
Solution
r = {-0.4285714286w, 0.8w}