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

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

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

Reorder the terms:
(p + -2q)(p + 2q) = 0

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

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

Reorder the terms:
(2pq + -2pq + p2 + -4q2) = 0

Combine like terms: 2pq + -2pq = 0
(0 + p2 + -4q2) = 0
(p2 + -4q2) = 0

Solving
p2 + -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.
p2 + -4q2 + 4q2 = 0 + 4q2

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

Simplifying
p2 = 4q2

Take the square root of each side:
p = {-2q, 2q}