(5p-2q)(5p+2q)=0

Solution for (5p-2q)(5p+2q)=0 equation:

Simplifying
(5p + -2q)(5p + 2q) = 0

Multiply (5p + -2q) * (5p + 2q)
(5p * (5p + 2q) + -2q * (5p + 2q)) = 0
((5p * 5p + 2q * 5p) + -2q * (5p + 2q)) = 0

Reorder the terms:
((10pq + 25p2) + -2q * (5p + 2q)) = 0
((10pq + 25p2) + -2q * (5p + 2q)) = 0
(10pq + 25p2 + (5p * -2q + 2q * -2q)) = 0
(10pq + 25p2 + (-10pq + -4q2)) = 0

Reorder the terms:
(10pq + -10pq + 25p2 + -4q2) = 0

Combine like terms: 10pq + -10pq = 0
(0 + 25p2 + -4q2) = 0
(25p2 + -4q2) = 0

Solving
25p2 + -4q2 = 0

Solving for variable 'p'.

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

Add '4q2' to each side of the equation.
25p2 + -4q2 + 4q2 = 0 + 4q2

Combine like terms: -4q2 + 4q2 = 0
25p2 + 0 = 0 + 4q2
25p2 = 0 + 4q2
Remove the zero:
25p2 = 4q2

Divide each side by '25'.
p2 = 0.16q2

Simplifying
p2 = 0.16q2

Take the square root of each side:
p = {-0.4q, 0.4q}