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Simplifying 3p2 + p = 3p + 16 Reorder the terms: p + 3p2 = 3p + 16 Reorder the terms: p + 3p2 = 16 + 3p Solving p + 3p2 = 16 + 3p Solving for variable 'p'. Reorder the terms: -16 + p + -3p + 3p2 = 16 + 3p + -16 + -3p Combine like terms: p + -3p = -2p -16 + -2p + 3p2 = 16 + 3p + -16 + -3p Reorder the terms: -16 + -2p + 3p2 = 16 + -16 + 3p + -3p Combine like terms: 16 + -16 = 0 -16 + -2p + 3p2 = 0 + 3p + -3p -16 + -2p + 3p2 = 3p + -3p Combine like terms: 3p + -3p = 0 -16 + -2p + 3p2 = 0 Factor a trinomial. (-2 + -1p)(8 + -3p) = 0Subproblem 1
Set the factor '(-2 + -1p)' equal to zero and attempt to solve: Simplifying -2 + -1p = 0 Solving -2 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1p = 0 + 2 -1p = 0 + 2 Combine like terms: 0 + 2 = 2 -1p = 2 Divide each side by '-1'. p = -2 Simplifying p = -2Subproblem 2
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 = 2.666666667Solution
p = {-2, 2.666666667}
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