(4p-3q)(9p+2q)=

Solution for (4p-3q)(9p+2q)= equation:

Simplifying
(4p + -3q)(9p + 2q) = 0

Multiply (4p + -3q) * (9p + 2q)
(4p * (9p + 2q) + -3q * (9p + 2q)) = 0
((9p * 4p + 2q * 4p) + -3q * (9p + 2q)) = 0

Reorder the terms:
((8pq + 36p2) + -3q * (9p + 2q)) = 0
((8pq + 36p2) + -3q * (9p + 2q)) = 0
(8pq + 36p2 + (9p * -3q + 2q * -3q)) = 0
(8pq + 36p2 + (-27pq + -6q2)) = 0

Reorder the terms:
(8pq + -27pq + 36p2 + -6q2) = 0

Combine like terms: 8pq + -27pq = -19pq
(-19pq + 36p2 + -6q2) = 0

Solving
-19pq + 36p2 + -6q2 = 0

Solving for variable 'p'.

Factor a trinomial.
(4p + -3q)(9p + 2q) = 0

Subproblem 1
Set the factor '(4p + -3q)' equal to zero and attempt to solve:

Simplifying
4p + -3q = 0

Solving
4p + -3q = 0

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

Add '3q' to each side of the equation.
4p + -3q + 3q = 0 + 3q

Combine like terms: -3q + 3q = 0
4p + 0 = 0 + 3q
4p = 0 + 3q
Remove the zero:
4p = 3q

Divide each side by '4'.
p = 0.75q

Simplifying
p = 0.75q
Subproblem 2
Set the factor '(9p + 2q)' equal to zero and attempt to solve:

Simplifying
9p + 2q = 0

Solving
9p + 2q = 0

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

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

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

Divide each side by '9'.
p = -0.2222222222q

Simplifying
p = -0.2222222222q
Solution
p = {0.75q, -0.2222222222q}