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Simplifying 3p2 = 15 + -4p Solving 3p2 = 15 + -4p Solving for variable 'p'. Reorder the terms: -15 + 4p + 3p2 = 15 + -4p + -15 + 4p Reorder the terms: -15 + 4p + 3p2 = 15 + -15 + -4p + 4p Combine like terms: 15 + -15 = 0 -15 + 4p + 3p2 = 0 + -4p + 4p -15 + 4p + 3p2 = -4p + 4p Combine like terms: -4p + 4p = 0 -15 + 4p + 3p2 = 0 Factor a trinomial. (-3 + -1p)(5 + -3p) = 0Subproblem 1
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 = -3Subproblem 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 = {-3, 1.666666667}
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