(5p+3q)(-2p+9q)=

Solution for (5p+3q)(-2p+9q)= equation:

Simplifying
(5p + 3q)(-2p + 9q) = 0

Multiply (5p + 3q) * (-2p + 9q)
(5p * (-2p + 9q) + 3q * (-2p + 9q)) = 0
((-2p * 5p + 9q * 5p) + 3q * (-2p + 9q)) = 0

Reorder the terms:
((45pq + -10p2) + 3q * (-2p + 9q)) = 0
((45pq + -10p2) + 3q * (-2p + 9q)) = 0
(45pq + -10p2 + (-2p * 3q + 9q * 3q)) = 0
(45pq + -10p2 + (-6pq + 27q2)) = 0

Reorder the terms:
(45pq + -6pq + -10p2 + 27q2) = 0

Combine like terms: 45pq + -6pq = 39pq
(39pq + -10p2 + 27q2) = 0

Solving
39pq + -10p2 + 27q2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-5p + -3q)(2p + -9q) = 0

Subproblem 1
Set the factor '(-5p + -3q)' equal to zero and attempt to solve:

Simplifying
-5p + -3q = 0

Solving
-5p + -3q = 0

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

Add '3q' to each side of the equation.
-5p + -3q + 3q = 0 + 3q

Combine like terms: -3q + 3q = 0
-5p + 0 = 0 + 3q
-5p = 0 + 3q
Remove the zero:
-5p = 3q

Divide each side by '-5'.
p = -0.6q

Simplifying
p = -0.6q
Subproblem 2
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
Solution
p = {-0.6q, 4.5q}