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

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

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

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

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

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

Reorder the terms:
((-24pw + -30p2) + 4w * (5p + 4w)) = 0
((-24pw + -30p2) + 4w * (5p + 4w)) = 0
(-24pw + -30p2 + (5p * 4w + 4w * 4w)) = 0
(-24pw + -30p2 + (20pw + 16w2)) = 0

Reorder the terms:
(-24pw + 20pw + -30p2 + 16w2) = 0

Combine like terms: -24pw + 20pw = -4pw
(-4pw + -30p2 + 16w2) = 0

Solving
-4pw + -30p2 + 16w2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2pw + -15p2 + 8w2) = 0

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

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

Simplifying
-5p + -4w = 0

Solving
-5p + -4w = 0

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

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

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

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

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

Simplifying
3p + -2w = 0

Solving
3p + -2w = 0

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

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

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

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

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