(2p+5q)x(3p-8q)=

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Solution for (2p+5q)x(3p-8q)= equation: 


Simplifying
(2p + 5q) * x(3p + -8q) = 0

Reorder the terms for easier multiplication:
x(2p + 5q)(3p + -8q) = 0

Multiply (2p + 5q) * (3p + -8q)
x(2p * (3p + -8q) + 5q * (3p + -8q)) = 0
x((3p * 2p + -8q * 2p) + 5q * (3p + -8q)) = 0

Reorder the terms:
x((-16pq + 6p2) + 5q * (3p + -8q)) = 0
x((-16pq + 6p2) + 5q * (3p + -8q)) = 0
x(-16pq + 6p2 + (3p * 5q + -8q * 5q)) = 0
x(-16pq + 6p2 + (15pq + -40q2)) = 0

Reorder the terms:
x(-16pq + 15pq + 6p2 + -40q2) = 0

Combine like terms: -16pq + 15pq = -1pq
x(-1pq + 6p2 + -40q2) = 0
(-1pq * x + 6p2 * x + -40q2 * x) = 0
(-1pqx + 6p2x + -40q2x) = 0

Solving
-1pqx + 6p2x + -40q2x = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1pq + 6p2 + -40q2) = 0

Factor a trinomial.
x((3p + -8q)(2p + 5q)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(3p + -8q)' equal to zero and attempt to solve:

Simplifying
3p + -8q = 0

Solving
3p + -8q = 0

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

Add '8q' to each side of the equation.
3p + -8q + 8q = 0 + 8q

Combine like terms: -8q + 8q = 0
3p + 0 = 0 + 8q
3p = 0 + 8q
Remove the zero:
3p = 8q

Divide each side by '3'.
p = 2.666666667q

Simplifying
p = 2.666666667q

Subproblem 3
Set the factor '(2p + 5q)' equal to zero and attempt to solve:

Simplifying
2p + 5q = 0

Solving
2p + 5q = 0

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

Add '-5q' to each side of the equation.
2p + 5q + -5q = 0 + -5q

Combine like terms: 5q + -5q = 0
2p + 0 = 0 + -5q
2p = 0 + -5q
Remove the zero:
2p = -5q

Divide each side by '2'.
p = -2.5q

Simplifying
p = -2.5q
Solution
p = {2.666666667q, -2.5q}

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