(2p-9q)(p+3q)=

Solution for (2p-9q)(p+3q)= equation:

Simplifying
(2p + -9q)(p + 3q) = 0

Multiply (2p + -9q) * (p + 3q)
(2p * (p + 3q) + -9q * (p + 3q)) = 0
((p * 2p + 3q * 2p) + -9q * (p + 3q)) = 0

Reorder the terms:
((6pq + 2p2) + -9q * (p + 3q)) = 0
((6pq + 2p2) + -9q * (p + 3q)) = 0
(6pq + 2p2 + (p * -9q + 3q * -9q)) = 0
(6pq + 2p2 + (-9pq + -27q2)) = 0

Reorder the terms:
(6pq + -9pq + 2p2 + -27q2) = 0

Combine like terms: 6pq + -9pq = -3pq
(-3pq + 2p2 + -27q2) = 0

Solving
-3pq + 2p2 + -27q2 = 0

Solving for variable 'p'.

Factor a trinomial.
(2p + -9q)(p + 3q) = 0

Subproblem 1
Set the factor '(2p + -9q)' equal to zero and attempt to solve:

Simplifying
2p + -9q = 0

Solving
2p + -9q = 0

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

Add '9q' to each side of the equation.
2p + -9q + 9q = 0 + 9q

Combine like terms: -9q + 9q = 0
2p + 0 = 0 + 9q
2p = 0 + 9q
Remove the zero:
2p = 9q

Divide each side by '2'.
p = 4.5q

Simplifying
p = 4.5q
Subproblem 2
Set the factor '(p + 3q)' equal to zero and attempt to solve:

Simplifying
p + 3q = 0

Solving
p + 3q = 0

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

Add '-3q' to each side of the equation.
p + 3q + -3q = 0 + -3q

Combine like terms: 3q + -3q = 0
p + 0 = 0 + -3q
p = 0 + -3q
Remove the zero:
p = -3q

Simplifying
p = -3q
Solution
p = {4.5q, -3q}