16p^2+79p+27=-5+7p

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Solution for 16p^2+79p+27=-5+7p equation:


Simplifying
16p2 + 79p + 27 = -5 + 7p

Reorder the terms:
27 + 79p + 16p2 = -5 + 7p

Solving
27 + 79p + 16p2 = -5 + 7p

Solving for variable 'p'.

Reorder the terms:
27 + 5 + 79p + -7p + 16p2 = -5 + 7p + 5 + -7p

Combine like terms: 27 + 5 = 32
32 + 79p + -7p + 16p2 = -5 + 7p + 5 + -7p

Combine like terms: 79p + -7p = 72p
32 + 72p + 16p2 = -5 + 7p + 5 + -7p

Reorder the terms:
32 + 72p + 16p2 = -5 + 5 + 7p + -7p

Combine like terms: -5 + 5 = 0
32 + 72p + 16p2 = 0 + 7p + -7p
32 + 72p + 16p2 = 7p + -7p

Combine like terms: 7p + -7p = 0
32 + 72p + 16p2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(4 + 9p + 2p2) = 0

Factor a trinomial.
8((4 + p)(1 + 2p)) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(4 + p)' equal to zero and attempt to solve: Simplifying 4 + p = 0 Solving 4 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + p = 0 + -4 p = 0 + -4 Combine like terms: 0 + -4 = -4 p = -4 Simplifying p = -4

Subproblem 2

Set the factor '(1 + 2p)' equal to zero and attempt to solve: Simplifying 1 + 2p = 0 Solving 1 + 2p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2p = 0 + -1 2p = 0 + -1 Combine like terms: 0 + -1 = -1 2p = -1 Divide each side by '2'. p = -0.5 Simplifying p = -0.5

Solution

p = {-4, -0.5}

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