2r^2+3pr-2p^2=0

Solution for 2r^2+3pr-2p^2=0 equation:

Simplifying
2r2 + 3pr + -2p2 = 0

Reorder the terms:
3pr + -2p2 + 2r2 = 0

Solving
3pr + -2p2 + 2r2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-2p + -1r)(p + -2r) = 0

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

Simplifying
-2p + -1r = 0

Solving
-2p + -1r = 0

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

Add 'r' to each side of the equation.
-2p + -1r + r = 0 + r

Combine like terms: -1r + r = 0
-2p + 0 = 0 + r
-2p = 0 + r
Remove the zero:
-2p = r

Divide each side by '-2'.
p = -0.5r

Simplifying
p = -0.5r
Subproblem 2
Set the factor '(p + -2r)' equal to zero and attempt to solve:

Simplifying
p + -2r = 0

Solving
p + -2r = 0

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

Add '2r' to each side of the equation.
p + -2r + 2r = 0 + 2r

Combine like terms: -2r + 2r = 0
p + 0 = 0 + 2r
p = 0 + 2r
Remove the zero:
p = 2r

Simplifying
p = 2r
Solution
p = {-0.5r, 2r}