(11p+4q)(-2p+8q)=

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Solution for (11p+4q)(-2p+8q)= equation: 


Simplifying
(11p + 4q)(-2p + 8q) = 0

Multiply (11p + 4q) * (-2p + 8q)
(11p * (-2p + 8q) + 4q * (-2p + 8q)) = 0
((-2p * 11p + 8q * 11p) + 4q * (-2p + 8q)) = 0

Reorder the terms:
((88pq + -22p2) + 4q * (-2p + 8q)) = 0
((88pq + -22p2) + 4q * (-2p + 8q)) = 0
(88pq + -22p2 + (-2p * 4q + 8q * 4q)) = 0
(88pq + -22p2 + (-8pq + 32q2)) = 0

Reorder the terms:
(88pq + -8pq + -22p2 + 32q2) = 0

Combine like terms: 88pq + -8pq = 80pq
(80pq + -22p2 + 32q2) = 0

Solving
80pq + -22p2 + 32q2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(40pq + -11p2 + 16q2) = 0

Factor a trinomial.
2((-11p + -4q)(p + -4q)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11p + -4q)' equal to zero and attempt to solve:

Simplifying
-11p + -4q = 0

Solving
-11p + -4q = 0

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

Add '4q' to each side of the equation.
-11p + -4q + 4q = 0 + 4q

Combine like terms: -4q + 4q = 0
-11p + 0 = 0 + 4q
-11p = 0 + 4q
Remove the zero:
-11p = 4q

Divide each side by '-11'.
p = -0.3636363636q

Simplifying
p = -0.3636363636q

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 = {-0.3636363636q, 4q}

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