=p^3-5p^2q-24pq^2

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Solution for =p^3-5p^2q-24pq^2 equation: 


Simplifying
0 = p3 + -5p2q + -24pq2

Reorder the terms:
0 = -24pq2 + -5p2q + p3

Solving
0 = -24pq2 + -5p2q + p3

Solving for variable 'p'.
Remove the zero:
24pq2 + 5p2q + -1p3 = -24pq2 + -5p2q + p3 + 24pq2 + 5p2q + -1p3

Reorder the terms:
24pq2 + 5p2q + -1p3 = -24pq2 + 24pq2 + -5p2q + 5p2q + p3 + -1p3

Combine like terms: -24pq2 + 24pq2 = 0
24pq2 + 5p2q + -1p3 = 0 + -5p2q + 5p2q + p3 + -1p3
24pq2 + 5p2q + -1p3 = -5p2q + 5p2q + p3 + -1p3

Combine like terms: -5p2q + 5p2q = 0
24pq2 + 5p2q + -1p3 = 0 + p3 + -1p3
24pq2 + 5p2q + -1p3 = p3 + -1p3

Combine like terms: p3 + -1p3 = 0
24pq2 + 5p2q + -1p3 = 0

Factor out the Greatest Common Factor (GCF), 'p'.
p(24q2 + 5pq + -1p2) = 0

Factor a trinomial.
p((8q + -1p)(3q + p)) = 0


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

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0

Subproblem 2
Set the factor '(8q + -1p)' equal to zero and attempt to solve:

Simplifying
8q + -1p = 0

Reorder the terms:
-1p + 8q = 0

Solving
-1p + 8q = 0

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

Add '-8q' to each side of the equation.
-1p + 8q + -8q = 0 + -8q

Combine like terms: 8q + -8q = 0
-1p + 0 = 0 + -8q
-1p = 0 + -8q
Remove the zero:
-1p = -8q

Divide each side by '-1'.
p = 8q

Simplifying
p = 8q

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

Simplifying
3q + p = 0

Reorder the terms:
p + 3q = 0

Solving
p + 3q = 0

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

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

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

Simplifying
p = -3q
Solution
p = {0, 8q, -3q}

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