(7p+5q)(-2p+6q)=

Solution for (7p+5q)(-2p+6q)= equation:

Simplifying
(7p + 5q)(-2p + 6q) = 0

Multiply (7p + 5q) * (-2p + 6q)
(7p * (-2p + 6q) + 5q * (-2p + 6q)) = 0
((-2p * 7p + 6q * 7p) + 5q * (-2p + 6q)) = 0

Reorder the terms:
((42pq + -14p2) + 5q * (-2p + 6q)) = 0
((42pq + -14p2) + 5q * (-2p + 6q)) = 0
(42pq + -14p2 + (-2p * 5q + 6q * 5q)) = 0
(42pq + -14p2 + (-10pq + 30q2)) = 0

Reorder the terms:
(42pq + -10pq + -14p2 + 30q2) = 0

Combine like terms: 42pq + -10pq = 32pq
(32pq + -14p2 + 30q2) = 0

Solving
32pq + -14p2 + 30q2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16pq + -7p2 + 15q2) = 0

Factor a trinomial.
2((-7p + -5q)(p + -3q)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7p + -5q)' equal to zero and attempt to solve:

Simplifying
-7p + -5q = 0

Solving
-7p + -5q = 0

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

Add '5q' to each side of the equation.
-7p + -5q + 5q = 0 + 5q

Combine like terms: -5q + 5q = 0
-7p + 0 = 0 + 5q
-7p = 0 + 5q
Remove the zero:
-7p = 5q

Divide each side by '-7'.
p = -0.7142857143q

Simplifying
p = -0.7142857143q
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 = {-0.7142857143q, 3q}