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

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

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

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

Reorder the terms:
((4pq + 6p2) + q(3p + 2q)) = 0
((4pq + 6p2) + q(3p + 2q)) = 0
(4pq + 6p2 + (3p * q + 2q * q)) = 0
(4pq + 6p2 + (3pq + 2q2)) = 0

Reorder the terms:
(4pq + 3pq + 6p2 + 2q2) = 0

Combine like terms: 4pq + 3pq = 7pq
(7pq + 6p2 + 2q2) = 0

Solving
7pq + 6p2 + 2q2 = 0

Solving for variable 'p'.

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

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

Simplifying
2p + q = 0

Solving
2p + q = 0

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

Add '-1q' to each side of the equation.
2p + q + -1q = 0 + -1q

Combine like terms: q + -1q = 0
2p + 0 = 0 + -1q
2p = 0 + -1q
Remove the zero:
2p = -1q

Divide each side by '2'.
p = -0.5q

Simplifying
p = -0.5q
Subproblem 2
Set the factor '(3p + 2q)' equal to zero and attempt to solve:

Simplifying
3p + 2q = 0

Solving
3p + 2q = 0

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

Add '-2q' to each side of the equation.
3p + 2q + -2q = 0 + -2q

Combine like terms: 2q + -2q = 0
3p + 0 = 0 + -2q
3p = 0 + -2q
Remove the zero:
3p = -2q

Divide each side by '3'.
p = -0.6666666667q

Simplifying
p = -0.6666666667q
Solution
p = {-0.5q, -0.6666666667q}