(10p+7q)(-2p+8q)=

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Solution for (10p+7q)(-2p+8q)= equation: 


Simplifying
(10p + 7q)(-2p + 8q) = 0

Multiply (10p + 7q) * (-2p + 8q)
(10p * (-2p + 8q) + 7q * (-2p + 8q)) = 0
((-2p * 10p + 8q * 10p) + 7q * (-2p + 8q)) = 0

Reorder the terms:
((80pq + -20p2) + 7q * (-2p + 8q)) = 0
((80pq + -20p2) + 7q * (-2p + 8q)) = 0
(80pq + -20p2 + (-2p * 7q + 8q * 7q)) = 0
(80pq + -20p2 + (-14pq + 56q2)) = 0

Reorder the terms:
(80pq + -14pq + -20p2 + 56q2) = 0

Combine like terms: 80pq + -14pq = 66pq
(66pq + -20p2 + 56q2) = 0

Solving
66pq + -20p2 + 56q2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(33pq + -10p2 + 28q2) = 0

Factor a trinomial.
2((-10p + -7q)(p + -4q)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10p + -7q)' equal to zero and attempt to solve:

Simplifying
-10p + -7q = 0

Solving
-10p + -7q = 0

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

Add '7q' to each side of the equation.
-10p + -7q + 7q = 0 + 7q

Combine like terms: -7q + 7q = 0
-10p + 0 = 0 + 7q
-10p = 0 + 7q
Remove the zero:
-10p = 7q

Divide each side by '-10'.
p = -0.7q

Simplifying
p = -0.7q

Subproblem 2
Set the factor '(p + -4q)' equal to zero and attempt to solve:

Simplifying
p + -4q = 0

Solving
p + -4q = 0

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

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

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

Simplifying
p = 4q
Solution
p = {-0.7q, 4q}

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