p^4=2p^3+15p^2

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Solution for p^4=2p^3+15p^2 equation: 


Simplifying
p4 = 2p3 + 15p2

Reorder the terms:
p4 = 15p2 + 2p3

Solving
p4 = 15p2 + 2p3

Solving for variable 'p'.

Reorder the terms:
-15p2 + -2p3 + p4 = 15p2 + 2p3 + -15p2 + -2p3

Reorder the terms:
-15p2 + -2p3 + p4 = 15p2 + -15p2 + 2p3 + -2p3

Combine like terms: 15p2 + -15p2 = 0
-15p2 + -2p3 + p4 = 0 + 2p3 + -2p3
-15p2 + -2p3 + p4 = 2p3 + -2p3

Combine like terms: 2p3 + -2p3 = 0
-15p2 + -2p3 + p4 = 0

Factor out the Greatest Common Factor (GCF), 'p2'.
p2(-15 + -2p + p2) = 0

Factor a trinomial.
p2((-3 + -1p)(5 + -1p)) = 0


Subproblem 1
Set the factor 'p2' equal to zero and attempt to solve:

Simplifying
p2 = 0

Solving
p2 = 0

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

Simplifying
p2 = 0

Take the square root of each side:
p = {0}

Subproblem 2
Set the factor '(-3 + -1p)' equal to zero and attempt to solve:

Simplifying
-3 + -1p = 0

Solving
-3 + -1p = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1p = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1p = 0 + 3
-1p = 0 + 3

Combine like terms: 0 + 3 = 3
-1p = 3

Divide each side by '-1'.
p = -3

Simplifying
p = -3

Subproblem 3
Set the factor '(5 + -1p)' equal to zero and attempt to solve:

Simplifying
5 + -1p = 0

Solving
5 + -1p = 0

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

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

Combine like terms: 5 + -5 = 0
0 + -1p = 0 + -5
-1p = 0 + -5

Combine like terms: 0 + -5 = -5
-1p = -5

Divide each side by '-1'.
p = 5

Simplifying
p = 5
Solution
p = {0, -3, 5}

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