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Simplifying 42p2 + 144p + 120 = 0 Reorder the terms: 120 + 144p + 42p2 = 0 Solving 120 + 144p + 42p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '6'. 6(20 + 24p + 7p2) = 0 Factor a trinomial. 6((2 + p)(10 + 7p)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(2 + p)' equal to zero and attempt to solve: Simplifying 2 + p = 0 Solving 2 + p = 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 + p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + p = 0 + -2 p = 0 + -2 Combine like terms: 0 + -2 = -2 p = -2 Simplifying p = -2Subproblem 2
Set the factor '(10 + 7p)' equal to zero and attempt to solve: Simplifying 10 + 7p = 0 Solving 10 + 7p = 0 Move all terms containing p to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 7p = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 7p = 0 + -10 7p = 0 + -10 Combine like terms: 0 + -10 = -10 7p = -10 Divide each side by '7'. p = -1.428571429 Simplifying p = -1.428571429Solution
p = {-2, -1.428571429}
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