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Simplifying 6p2 + -18p + 12 = -5p + 3p2 Reorder the terms: 12 + -18p + 6p2 = -5p + 3p2 Solving 12 + -18p + 6p2 = -5p + 3p2 Solving for variable 'p'. Reorder the terms: 12 + -18p + 5p + 6p2 + -3p2 = -5p + 3p2 + 5p + -3p2 Combine like terms: -18p + 5p = -13p 12 + -13p + 6p2 + -3p2 = -5p + 3p2 + 5p + -3p2 Combine like terms: 6p2 + -3p2 = 3p2 12 + -13p + 3p2 = -5p + 3p2 + 5p + -3p2 Reorder the terms: 12 + -13p + 3p2 = -5p + 5p + 3p2 + -3p2 Combine like terms: -5p + 5p = 0 12 + -13p + 3p2 = 0 + 3p2 + -3p2 12 + -13p + 3p2 = 3p2 + -3p2 Combine like terms: 3p2 + -3p2 = 0 12 + -13p + 3p2 = 0 Factor a trinomial. (4 + -3p)(3 + -1p) = 0Subproblem 1
Set the factor '(4 + -3p)' equal to zero and attempt to solve: Simplifying 4 + -3p = 0 Solving 4 + -3p = 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 + -3p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3p = 0 + -4 -3p = 0 + -4 Combine like terms: 0 + -4 = -4 -3p = -4 Divide each side by '-3'. p = 1.333333333 Simplifying p = 1.333333333Subproblem 2
Set the factor '(3 + -1p)' equal to zero and attempt to solve: Simplifying 3 + -1p = 0 Solving 3 + -1p = 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 + -1p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1p = 0 + -3 -1p = 0 + -3 Combine like terms: 0 + -3 = -3 -1p = -3 Divide each side by '-1'. p = 3 Simplifying p = 3Solution
p = {1.333333333, 3}
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