(10p+6q)(-2p+6q)=

Solution for (10p+6q)(-2p+6q)= equation:

Simplifying
(10p + 6q)(-2p + 6q) = 0

Multiply (10p + 6q) * (-2p + 6q)
(10p * (-2p + 6q) + 6q * (-2p + 6q)) = 0
((-2p * 10p + 6q * 10p) + 6q * (-2p + 6q)) = 0

Reorder the terms:
((60pq + -20p2) + 6q * (-2p + 6q)) = 0
((60pq + -20p2) + 6q * (-2p + 6q)) = 0
(60pq + -20p2 + (-2p * 6q + 6q * 6q)) = 0
(60pq + -20p2 + (-12pq + 36q2)) = 0

Reorder the terms:
(60pq + -12pq + -20p2 + 36q2) = 0

Combine like terms: 60pq + -12pq = 48pq
(48pq + -20p2 + 36q2) = 0

Solving
48pq + -20p2 + 36q2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '4'.
4(12pq + -5p2 + 9q2) = 0

Factor a trinomial.
4((-5p + -3q)(p + -3q)) = 0

Ignore the factor 4.
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 '(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 = {-0.6q, 3q}