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Simplifying 18p2 + 102p + -540 = 0 Reorder the terms: -540 + 102p + 18p2 = 0 Solving -540 + 102p + 18p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '6'. 6(-90 + 17p + 3p2) = 0 Factor a trinomial. 6((-9 + -1p)(10 + -3p)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-9 + -1p)' equal to zero and attempt to solve: Simplifying -9 + -1p = 0 Solving -9 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1p = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1p = 0 + 9 -1p = 0 + 9 Combine like terms: 0 + 9 = 9 -1p = 9 Divide each side by '-1'. p = -9 Simplifying p = -9Subproblem 2
Set the factor '(10 + -3p)' equal to zero and attempt to solve: Simplifying 10 + -3p = 0 Solving 10 + -3p = 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 + -3p = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3p = 0 + -10 -3p = 0 + -10 Combine like terms: 0 + -10 = -10 -3p = -10 Divide each side by '-3'. p = 3.333333333 Simplifying p = 3.333333333Solution
p = {-9, 3.333333333}
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