6p^2+8=-19p

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Solution for 6p^2+8=-19p equation:


Simplifying
6p2 + 8 = -19p

Reorder the terms:
8 + 6p2 = -19p

Solving
8 + 6p2 = -19p

Solving for variable 'p'.

Reorder the terms:
8 + 19p + 6p2 = -19p + 19p

Combine like terms: -19p + 19p = 0
8 + 19p + 6p2 = 0

Factor a trinomial.
(8 + 3p)(1 + 2p) = 0

Subproblem 1

Set the factor '(8 + 3p)' equal to zero and attempt to solve: Simplifying 8 + 3p = 0 Solving 8 + 3p = 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 + 3p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3p = 0 + -8 3p = 0 + -8 Combine like terms: 0 + -8 = -8 3p = -8 Divide each side by '3'. p = -2.666666667 Simplifying p = -2.666666667

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 = {-2.666666667, -0.5}

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