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Simplifying 21p2 + 119p + 140 = 0 Reorder the terms: 140 + 119p + 21p2 = 0 Solving 140 + 119p + 21p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '7'. 7(20 + 17p + 3p2) = 0 Factor a trinomial. 7((4 + p)(5 + 3p)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(4 + p)' equal to zero and attempt to solve: Simplifying 4 + p = 0 Solving 4 + p = 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 + p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + p = 0 + -4 p = 0 + -4 Combine like terms: 0 + -4 = -4 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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