(10p+2q)(-4p+8q)=

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Solution for (10p+2q)(-4p+8q)= equation: 


Simplifying
(10p + 2q)(-4p + 8q) = 0

Multiply (10p + 2q) * (-4p + 8q)
(10p * (-4p + 8q) + 2q * (-4p + 8q)) = 0
((-4p * 10p + 8q * 10p) + 2q * (-4p + 8q)) = 0

Reorder the terms:
((80pq + -40p2) + 2q * (-4p + 8q)) = 0
((80pq + -40p2) + 2q * (-4p + 8q)) = 0
(80pq + -40p2 + (-4p * 2q + 8q * 2q)) = 0
(80pq + -40p2 + (-8pq + 16q2)) = 0

Reorder the terms:
(80pq + -8pq + -40p2 + 16q2) = 0

Combine like terms: 80pq + -8pq = 72pq
(72pq + -40p2 + 16q2) = 0

Solving
72pq + -40p2 + 16q2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '8'.
8(9pq + -5p2 + 2q2) = 0

Factor a trinomial.
8((-5p + -1q)(p + -2q)) = 0

Ignore the factor 8.

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

Simplifying
-5p + -1q = 0

Solving
-5p + -1q = 0

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

Add 'q' to each side of the equation.
-5p + -1q + q = 0 + q

Combine like terms: -1q + q = 0
-5p + 0 = 0 + q
-5p = 0 + q
Remove the zero:
-5p = q

Divide each side by '-5'.
p = -0.2q

Simplifying
p = -0.2q

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

Simplifying
p + -2q = 0

Solving
p + -2q = 0

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

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

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

Simplifying
p = 2q
Solution
p = {-0.2q, 2q}

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