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Simplifying 90p2 + 114p + -48 = 0 Reorder the terms: -48 + 114p + 90p2 = 0 Solving -48 + 114p + 90p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '6'. 6(-8 + 19p + 15p2) = 0 Factor a trinomial. 6((-8 + -5p)(1 + -3p)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-8 + -5p)' equal to zero and attempt to solve: Simplifying -8 + -5p = 0 Solving -8 + -5p = 0 Move all terms containing p to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -5p = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5p = 0 + 8 -5p = 0 + 8 Combine like terms: 0 + 8 = 8 -5p = 8 Divide each side by '-5'. p = -1.6 Simplifying p = -1.6Subproblem 2
Set the factor '(1 + -3p)' equal to zero and attempt to solve: Simplifying 1 + -3p = 0 Solving 1 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3p = 0 + -1 -3p = 0 + -1 Combine like terms: 0 + -1 = -1 -3p = -1 Divide each side by '-3'. p = 0.3333333333 Simplifying p = 0.3333333333Solution
p = {-1.6, 0.3333333333}
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