(4r-6p)(4r+5p)=

Solution for (4r-6p)(4r+5p)= equation:

Simplifying
(4r + -6p)(4r + 5p) = 0

Reorder the terms:
(-6p + 4r)(4r + 5p) = 0

Reorder the terms:
(-6p + 4r)(5p + 4r) = 0

Multiply (-6p + 4r) * (5p + 4r)
(-6p * (5p + 4r) + 4r * (5p + 4r)) = 0
((5p * -6p + 4r * -6p) + 4r * (5p + 4r)) = 0

Reorder the terms:
((-24pr + -30p2) + 4r * (5p + 4r)) = 0
((-24pr + -30p2) + 4r * (5p + 4r)) = 0
(-24pr + -30p2 + (5p * 4r + 4r * 4r)) = 0
(-24pr + -30p2 + (20pr + 16r2)) = 0

Reorder the terms:
(-24pr + 20pr + -30p2 + 16r2) = 0

Combine like terms: -24pr + 20pr = -4pr
(-4pr + -30p2 + 16r2) = 0

Solving
-4pr + -30p2 + 16r2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2pr + -15p2 + 8r2) = 0

Factor a trinomial.
2((-5p + -4r)(3p + -2r)) = 0

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

Simplifying
-5p + -4r = 0

Solving
-5p + -4r = 0

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

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

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

Divide each side by '-5'.
p = -0.8r

Simplifying
p = -0.8r
Subproblem 2
Set the factor '(3p + -2r)' equal to zero and attempt to solve:

Simplifying
3p + -2r = 0

Solving
3p + -2r = 0

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

Add '2r' to each side of the equation.
3p + -2r + 2r = 0 + 2r

Combine like terms: -2r + 2r = 0
3p + 0 = 0 + 2r
3p = 0 + 2r
Remove the zero:
3p = 2r

Divide each side by '3'.
p = 0.6666666667r

Simplifying
p = 0.6666666667r
Solution
p = {-0.8r, 0.6666666667r}