(4r-3p)(4r+2p)=

Solution for (4r-3p)(4r+2p)= equation:

Simplifying
(4r + -3p)(4r + 2p) = 0

Reorder the terms:
(-3p + 4r)(4r + 2p) = 0

Reorder the terms:
(-3p + 4r)(2p + 4r) = 0

Multiply (-3p + 4r) * (2p + 4r)
(-3p * (2p + 4r) + 4r * (2p + 4r)) = 0
((2p * -3p + 4r * -3p) + 4r * (2p + 4r)) = 0

Reorder the terms:
((-12pr + -6p2) + 4r * (2p + 4r)) = 0
((-12pr + -6p2) + 4r * (2p + 4r)) = 0
(-12pr + -6p2 + (2p * 4r + 4r * 4r)) = 0
(-12pr + -6p2 + (8pr + 16r2)) = 0

Reorder the terms:
(-12pr + 8pr + -6p2 + 16r2) = 0

Combine like terms: -12pr + 8pr = -4pr
(-4pr + -6p2 + 16r2) = 0

Solving
-4pr + -6p2 + 16r2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2pr + -3p2 + 8r2) = 0

Factor a trinomial.
2((-1p + -2r)(3p + -4r)) = 0

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

Simplifying
-1p + -2r = 0

Solving
-1p + -2r = 0

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

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

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

Divide each side by '-1'.
p = -2r

Simplifying
p = -2r
Subproblem 2
Set the factor '(3p + -4r)' equal to zero and attempt to solve:

Simplifying
3p + -4r = 0

Solving
3p + -4r = 0

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

Add '4r' to each side of the equation.
3p + -4r + 4r = 0 + 4r

Combine like terms: -4r + 4r = 0
3p + 0 = 0 + 4r
3p = 0 + 4r
Remove the zero:
3p = 4r

Divide each side by '3'.
p = 1.333333333r

Simplifying
p = 1.333333333r
Solution
p = {-2r, 1.333333333r}