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

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

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

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

Reorder the terms:
((-20ap + 16a2) + 5p * (4a + -5p)) = 0
((-20ap + 16a2) + 5p * (4a + -5p)) = 0
(-20ap + 16a2 + (4a * 5p + -5p * 5p)) = 0
(-20ap + 16a2 + (20ap + -25p2)) = 0

Reorder the terms:
(-20ap + 20ap + 16a2 + -25p2) = 0

Combine like terms: -20ap + 20ap = 0
(0 + 16a2 + -25p2) = 0
(16a2 + -25p2) = 0

Solving
16a2 + -25p2 = 0

Solving for variable 'a'.

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

Add '25p2' to each side of the equation.
16a2 + -25p2 + 25p2 = 0 + 25p2

Combine like terms: -25p2 + 25p2 = 0
16a2 + 0 = 0 + 25p2
16a2 = 0 + 25p2
Remove the zero:
16a2 = 25p2

Divide each side by '16'.
a2 = 1.5625p2

Simplifying
a2 = 1.5625p2

Take the square root of each side:
a = {-1.25p, 1.25p}