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Simplifying 48p2 + 114p + -90 = 0 Reorder the terms: -90 + 114p + 48p2 = 0 Solving -90 + 114p + 48p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '6'. 6(-15 + 19p + 8p2) = 0 Factor a trinomial. 6((-3 + -1p)(5 + -8p)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + -1p)' equal to zero and attempt to solve: Simplifying -3 + -1p = 0 Solving -3 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1p = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1p = 0 + 3 -1p = 0 + 3 Combine like terms: 0 + 3 = 3 -1p = 3 Divide each side by '-1'. p = -3 Simplifying p = -3Subproblem 2
Set the factor '(5 + -8p)' equal to zero and attempt to solve: Simplifying 5 + -8p = 0 Solving 5 + -8p = 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 + -8p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8p = 0 + -5 -8p = 0 + -5 Combine like terms: 0 + -5 = -5 -8p = -5 Divide each side by '-8'. p = 0.625 Simplifying p = 0.625Solution
p = {-3, 0.625}
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