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Simplifying 5p2 + -16p + 15 = 4p + -5 Reorder the terms: 15 + -16p + 5p2 = 4p + -5 Reorder the terms: 15 + -16p + 5p2 = -5 + 4p Solving 15 + -16p + 5p2 = -5 + 4p Solving for variable 'p'. Reorder the terms: 15 + 5 + -16p + -4p + 5p2 = -5 + 4p + 5 + -4p Combine like terms: 15 + 5 = 20 20 + -16p + -4p + 5p2 = -5 + 4p + 5 + -4p Combine like terms: -16p + -4p = -20p 20 + -20p + 5p2 = -5 + 4p + 5 + -4p Reorder the terms: 20 + -20p + 5p2 = -5 + 5 + 4p + -4p Combine like terms: -5 + 5 = 0 20 + -20p + 5p2 = 0 + 4p + -4p 20 + -20p + 5p2 = 4p + -4p Combine like terms: 4p + -4p = 0 20 + -20p + 5p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(4 + -4p + p2) = 0 Factor a trinomial. 5((2 + -1p)(2 + -1p)) = 0 Ignore the factor 5.Subproblem 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 '(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 = 2Solution
p = {2, 2}
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