(5r-3p)(5r+2p)=

Solution for (5r-3p)(5r+2p)= equation:

Simplifying
(5r + -3p)(5r + 2p) = 0

Reorder the terms:
(-3p + 5r)(5r + 2p) = 0

Reorder the terms:
(-3p + 5r)(2p + 5r) = 0

Multiply (-3p + 5r) * (2p + 5r)
(-3p * (2p + 5r) + 5r * (2p + 5r)) = 0
((2p * -3p + 5r * -3p) + 5r * (2p + 5r)) = 0

Reorder the terms:
((-15pr + -6p2) + 5r * (2p + 5r)) = 0
((-15pr + -6p2) + 5r * (2p + 5r)) = 0
(-15pr + -6p2 + (2p * 5r + 5r * 5r)) = 0
(-15pr + -6p2 + (10pr + 25r2)) = 0

Reorder the terms:
(-15pr + 10pr + -6p2 + 25r2) = 0

Combine like terms: -15pr + 10pr = -5pr
(-5pr + -6p2 + 25r2) = 0

Solving
-5pr + -6p2 + 25r2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-2p + -5r)(3p + -5r) = 0

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

Simplifying
-2p + -5r = 0

Solving
-2p + -5r = 0

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

Add '5r' to each side of the equation.
-2p + -5r + 5r = 0 + 5r

Combine like terms: -5r + 5r = 0
-2p + 0 = 0 + 5r
-2p = 0 + 5r
Remove the zero:
-2p = 5r

Divide each side by '-2'.
p = -2.5r

Simplifying
p = -2.5r
Subproblem 2
Set the factor '(3p + -5r)' equal to zero and attempt to solve:

Simplifying
3p + -5r = 0

Solving
3p + -5r = 0

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

Add '5r' to each side of the equation.
3p + -5r + 5r = 0 + 5r

Combine like terms: -5r + 5r = 0
3p + 0 = 0 + 5r
3p = 0 + 5r
Remove the zero:
3p = 5r

Divide each side by '3'.
p = 1.666666667r

Simplifying
p = 1.666666667r
Solution
p = {-2.5r, 1.666666667r}