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

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

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

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

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

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

Reorder the terms:
((-12pv + -6p2) + 4v * (2p + 4v)) = 0
((-12pv + -6p2) + 4v * (2p + 4v)) = 0
(-12pv + -6p2 + (2p * 4v + 4v * 4v)) = 0
(-12pv + -6p2 + (8pv + 16v2)) = 0

Reorder the terms:
(-12pv + 8pv + -6p2 + 16v2) = 0

Combine like terms: -12pv + 8pv = -4pv
(-4pv + -6p2 + 16v2) = 0

Solving
-4pv + -6p2 + 16v2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2pv + -3p2 + 8v2) = 0

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

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

Simplifying
-1p + -2v = 0

Solving
-1p + -2v = 0

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

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

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

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

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

Simplifying
3p + -4v = 0

Solving
3p + -4v = 0

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

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

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

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

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