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

Solution for (4r+5p)(4r-5p)=0 equation:

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

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

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

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

Reorder the terms:
((20pr + -25p2) + 4r * (-5p + 4r)) = 0
((20pr + -25p2) + 4r * (-5p + 4r)) = 0
(20pr + -25p2 + (-5p * 4r + 4r * 4r)) = 0
(20pr + -25p2 + (-20pr + 16r2)) = 0

Reorder the terms:
(20pr + -20pr + -25p2 + 16r2) = 0

Combine like terms: 20pr + -20pr = 0
(0 + -25p2 + 16r2) = 0
(-25p2 + 16r2) = 0

Solving
-25p2 + 16r2 = 0

Solving for variable 'p'.

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

Add '-16r2' to each side of the equation.
-25p2 + 16r2 + -16r2 = 0 + -16r2

Combine like terms: 16r2 + -16r2 = 0
-25p2 + 0 = 0 + -16r2
-25p2 = 0 + -16r2
Remove the zero:
-25p2 = -16r2

Divide each side by '-25'.
p2 = 0.64r2

Simplifying
p2 = 0.64r2

Take the square root of each side:
p = {-0.8r, 0.8r}