(3p+q)(3p-q)=

Solution for (3p+q)(3p-q)= equation:

Simplifying
(3p + q)(3p + -1q) = 0

Multiply (3p + q) * (3p + -1q)
(3p * (3p + -1q) + q(3p + -1q)) = 0
((3p * 3p + -1q * 3p) + q(3p + -1q)) = 0

Reorder the terms:
((-3pq + 9p2) + q(3p + -1q)) = 0
((-3pq + 9p2) + q(3p + -1q)) = 0
(-3pq + 9p2 + (3p * q + -1q * q)) = 0
(-3pq + 9p2 + (3pq + -1q2)) = 0

Reorder the terms:
(-3pq + 3pq + 9p2 + -1q2) = 0

Combine like terms: -3pq + 3pq = 0
(0 + 9p2 + -1q2) = 0
(9p2 + -1q2) = 0

Solving
9p2 + -1q2 = 0

Solving for variable 'p'.

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

Add 'q2' to each side of the equation.
9p2 + -1q2 + q2 = 0 + q2

Combine like terms: -1q2 + q2 = 0
9p2 + 0 = 0 + q2
9p2 = 0 + q2
Remove the zero:
9p2 = q2

Divide each side by '9'.
p2 = 0.1111111111q2

Simplifying
p2 = 0.1111111111q2

Take the square root of each side:
p = {-0.333333333q, 0.333333333q}