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Simplifying 2p2 = 12 + -5p Solving 2p2 = 12 + -5p Solving for variable 'p'. Reorder the terms: -12 + 5p + 2p2 = 12 + -5p + -12 + 5p Reorder the terms: -12 + 5p + 2p2 = 12 + -12 + -5p + 5p Combine like terms: 12 + -12 = 0 -12 + 5p + 2p2 = 0 + -5p + 5p -12 + 5p + 2p2 = -5p + 5p Combine like terms: -5p + 5p = 0 -12 + 5p + 2p2 = 0 Factor a trinomial. (-4 + -1p)(3 + -2p) = 0Subproblem 1
Set the factor '(-4 + -1p)' equal to zero and attempt to solve: Simplifying -4 + -1p = 0 Solving -4 + -1p = 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 + -1p = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1p = 0 + 4 -1p = 0 + 4 Combine like terms: 0 + 4 = 4 -1p = 4 Divide each side by '-1'. p = -4 Simplifying p = -4Subproblem 2
Set the factor '(3 + -2p)' equal to zero and attempt to solve: Simplifying 3 + -2p = 0 Solving 3 + -2p = 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 + -2p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2p = 0 + -3 -2p = 0 + -3 Combine like terms: 0 + -3 = -3 -2p = -3 Divide each side by '-2'. p = 1.5 Simplifying p = 1.5Solution
p = {-4, 1.5}
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