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

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

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

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

Reorder the terms:
((25pq + 10p2) + 3q * (2p + 5q)) = 0
((25pq + 10p2) + 3q * (2p + 5q)) = 0
(25pq + 10p2 + (2p * 3q + 5q * 3q)) = 0
(25pq + 10p2 + (6pq + 15q2)) = 0

Reorder the terms:
(25pq + 6pq + 10p2 + 15q2) = 0

Combine like terms: 25pq + 6pq = 31pq
(31pq + 10p2 + 15q2) = 0

Solving
31pq + 10p2 + 15q2 = 0

Solving for variable 'p'.

Factor a trinomial.
(5p + 3q)(2p + 5q) = 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 + 5q)' equal to zero and attempt to solve:

Simplifying
2p + 5q = 0

Solving
2p + 5q = 0

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

Add '-5q' to each side of the equation.
2p + 5q + -5q = 0 + -5q

Combine like terms: 5q + -5q = 0
2p + 0 = 0 + -5q
2p = 0 + -5q
Remove the zero:
2p = -5q

Divide each side by '2'.
p = -2.5q

Simplifying
p = -2.5q
Solution
p = {-0.6q, -2.5q}