(5p+8q)(9p-2q)=

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Solution for (5p+8q)(9p-2q)= equation: 


Simplifying
(5p + 8q)(9p + -2q) = 0

Multiply (5p + 8q) * (9p + -2q)
(5p * (9p + -2q) + 8q * (9p + -2q)) = 0
((9p * 5p + -2q * 5p) + 8q * (9p + -2q)) = 0

Reorder the terms:
((-10pq + 45p2) + 8q * (9p + -2q)) = 0
((-10pq + 45p2) + 8q * (9p + -2q)) = 0
(-10pq + 45p2 + (9p * 8q + -2q * 8q)) = 0
(-10pq + 45p2 + (72pq + -16q2)) = 0

Reorder the terms:
(-10pq + 72pq + 45p2 + -16q2) = 0

Combine like terms: -10pq + 72pq = 62pq
(62pq + 45p2 + -16q2) = 0

Solving
62pq + 45p2 + -16q2 = 0

Solving for variable 'p'.

Factor a trinomial.
(9p + -2q)(5p + 8q) = 0


Subproblem 1
Set the factor '(9p + -2q)' equal to zero and attempt to solve:

Simplifying
9p + -2q = 0

Solving
9p + -2q = 0

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

Add '2q' to each side of the equation.
9p + -2q + 2q = 0 + 2q

Combine like terms: -2q + 2q = 0
9p + 0 = 0 + 2q
9p = 0 + 2q
Remove the zero:
9p = 2q

Divide each side by '9'.
p = 0.2222222222q

Simplifying
p = 0.2222222222q

Subproblem 2
Set the factor '(5p + 8q)' equal to zero and attempt to solve:

Simplifying
5p + 8q = 0

Solving
5p + 8q = 0

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

Add '-8q' to each side of the equation.
5p + 8q + -8q = 0 + -8q

Combine like terms: 8q + -8q = 0
5p + 0 = 0 + -8q
5p = 0 + -8q
Remove the zero:
5p = -8q

Divide each side by '5'.
p = -1.6q

Simplifying
p = -1.6q
Solution
p = {0.2222222222q, -1.6q}

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