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Simplifying 3p(p + 2) = 20 + -1p Reorder the terms: 3p(2 + p) = 20 + -1p (2 * 3p + p * 3p) = 20 + -1p (6p + 3p2) = 20 + -1p Solving 6p + 3p2 = 20 + -1p Solving for variable 'p'. Reorder the terms: -20 + 6p + p + 3p2 = 20 + -1p + -20 + p Combine like terms: 6p + p = 7p -20 + 7p + 3p2 = 20 + -1p + -20 + p Reorder the terms: -20 + 7p + 3p2 = 20 + -20 + -1p + p Combine like terms: 20 + -20 = 0 -20 + 7p + 3p2 = 0 + -1p + p -20 + 7p + 3p2 = -1p + p Combine like terms: -1p + p = 0 -20 + 7p + 3p2 = 0 Factor a trinomial. (-4 + -1p)(5 + -3p) = 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 '(5 + -3p)' equal to zero and attempt to solve: Simplifying 5 + -3p = 0 Solving 5 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3p = 0 + -5 -3p = 0 + -5 Combine like terms: 0 + -5 = -5 -3p = -5 Divide each side by '-3'. p = 1.666666667 Simplifying p = 1.666666667Solution
p = {-4, 1.666666667}
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