(5r-4p)(5r+3p)=

Solution for (5r-4p)(5r+3p)= equation:

Simplifying
(5r + -4p)(5r + 3p) = 0

Reorder the terms:
(-4p + 5r)(5r + 3p) = 0

Reorder the terms:
(-4p + 5r)(3p + 5r) = 0

Multiply (-4p + 5r) * (3p + 5r)
(-4p * (3p + 5r) + 5r * (3p + 5r)) = 0
((3p * -4p + 5r * -4p) + 5r * (3p + 5r)) = 0

Reorder the terms:
((-20pr + -12p2) + 5r * (3p + 5r)) = 0
((-20pr + -12p2) + 5r * (3p + 5r)) = 0
(-20pr + -12p2 + (3p * 5r + 5r * 5r)) = 0
(-20pr + -12p2 + (15pr + 25r2)) = 0

Reorder the terms:
(-20pr + 15pr + -12p2 + 25r2) = 0

Combine like terms: -20pr + 15pr = -5pr
(-5pr + -12p2 + 25r2) = 0

Solving
-5pr + -12p2 + 25r2 = 0

Solving for variable 'p'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(4p + -5r)' equal to zero and attempt to solve:

Simplifying
4p + -5r = 0

Solving
4p + -5r = 0

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

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

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

Divide each side by '4'.
p = 1.25r

Simplifying
p = 1.25r
Solution
p = {-1.666666667r, 1.25r}