r^2+3rp-40p^2=

Solution for r^2+3rp-40p^2= equation:

Simplifying
r2 + 3rp + -40p2 = 0

Reorder the terms:
3pr + -40p2 + r2 = 0

Solving
3pr + -40p2 + r2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-8p + -1r)(5p + -1r) = 0

Subproblem 1
Set the factor '(-8p + -1r)' equal to zero and attempt to solve:

Simplifying
-8p + -1r = 0

Solving
-8p + -1r = 0

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

Add 'r' to each side of the equation.
-8p + -1r + r = 0 + r

Combine like terms: -1r + r = 0
-8p + 0 = 0 + r
-8p = 0 + r
Remove the zero:
-8p = r

Divide each side by '-8'.
p = -0.125r

Simplifying
p = -0.125r
Subproblem 2
Set the factor '(5p + -1r)' equal to zero and attempt to solve:

Simplifying
5p + -1r = 0

Solving
5p + -1r = 0

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

Add 'r' to each side of the equation.
5p + -1r + r = 0 + r

Combine like terms: -1r + r = 0
5p + 0 = 0 + r
5p = 0 + r
Remove the zero:
5p = r

Divide each side by '5'.
p = 0.2r

Simplifying
p = 0.2r
Solution
p = {-0.125r, 0.2r}