(p+13q)(p-13q)=0

Solution for (p+13q)(p-13q)=0 equation:

Simplifying
(p + 13q)(p + -13q) = 0

Multiply (p + 13q) * (p + -13q)
(p(p + -13q) + 13q * (p + -13q)) = 0
((p * p + -13q * p) + 13q * (p + -13q)) = 0

Reorder the terms:
((-13pq + p2) + 13q * (p + -13q)) = 0
((-13pq + p2) + 13q * (p + -13q)) = 0
(-13pq + p2 + (p * 13q + -13q * 13q)) = 0
(-13pq + p2 + (13pq + -169q2)) = 0

Reorder the terms:
(-13pq + 13pq + p2 + -169q2) = 0

Combine like terms: -13pq + 13pq = 0
(0 + p2 + -169q2) = 0
(p2 + -169q2) = 0

Solving
p2 + -169q2 = 0

Solving for variable 'p'.

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

Add '169q2' to each side of the equation.
p2 + -169q2 + 169q2 = 0 + 169q2

Combine like terms: -169q2 + 169q2 = 0
p2 + 0 = 0 + 169q2
p2 = 0 + 169q2
Remove the zero:
p2 = 169q2

Simplifying
p2 = 169q2

Take the square root of each side:
p = {-13q, 13q}