2p^3=2p^2+112p

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Solution for 2p^3=2p^2+112p equation:


Simplifying
2p3 = 2p2 + 112p

Reorder the terms:
2p3 = 112p + 2p2

Solving
2p3 = 112p + 2p2

Solving for variable 'p'.

Reorder the terms:
-112p + -2p2 + 2p3 = 112p + 2p2 + -112p + -2p2

Reorder the terms:
-112p + -2p2 + 2p3 = 112p + -112p + 2p2 + -2p2

Combine like terms: 112p + -112p = 0
-112p + -2p2 + 2p3 = 0 + 2p2 + -2p2
-112p + -2p2 + 2p3 = 2p2 + -2p2

Combine like terms: 2p2 + -2p2 = 0
-112p + -2p2 + 2p3 = 0

Factor out the Greatest Common Factor (GCF), '2p'.
2p(-56 + -1p + p2) = 0

Factor a trinomial.
2p((-7 + -1p)(8 + -1p)) = 0

Ignore the factor 2.

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 '(-7 + -1p)' equal to zero and attempt to solve: Simplifying -7 + -1p = 0 Solving -7 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1p = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1p = 0 + 7 -1p = 0 + 7 Combine like terms: 0 + 7 = 7 -1p = 7 Divide each side by '-1'. p = -7 Simplifying p = -7

Subproblem 3

Set the factor '(8 + -1p)' equal to zero and attempt to solve: Simplifying 8 + -1p = 0 Solving 8 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1p = 0 + -8 -1p = 0 + -8 Combine like terms: 0 + -8 = -8 -1p = -8 Divide each side by '-1'. p = 8 Simplifying p = 8

Solution

p = {0, -7, 8}

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