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Simplifying 12p2 + -77p + 210 = 5p2 Reorder the terms: 210 + -77p + 12p2 = 5p2 Solving 210 + -77p + 12p2 = 5p2 Solving for variable 'p'. Combine like terms: 12p2 + -5p2 = 7p2 210 + -77p + 7p2 = 5p2 + -5p2 Combine like terms: 5p2 + -5p2 = 0 210 + -77p + 7p2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(30 + -11p + p2) = 0 Factor a trinomial. 7((5 + -1p)(6 + -1p)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(5 + -1p)' equal to zero and attempt to solve: Simplifying 5 + -1p = 0 Solving 5 + -1p = 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 + -1p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1p = 0 + -5 -1p = 0 + -5 Combine like terms: 0 + -5 = -5 -1p = -5 Divide each side by '-1'. p = 5 Simplifying p = 5Subproblem 2
Set the factor '(6 + -1p)' equal to zero and attempt to solve: Simplifying 6 + -1p = 0 Solving 6 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1p = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1p = 0 + -6 -1p = 0 + -6 Combine like terms: 0 + -6 = -6 -1p = -6 Divide each side by '-1'. p = 6 Simplifying p = 6Solution
p = {5, 6}
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