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Simplifying 24p2 = 20 + -28p Solving 24p2 = 20 + -28p Solving for variable 'p'. Reorder the terms: -20 + 28p + 24p2 = 20 + -28p + -20 + 28p Reorder the terms: -20 + 28p + 24p2 = 20 + -20 + -28p + 28p Combine like terms: 20 + -20 = 0 -20 + 28p + 24p2 = 0 + -28p + 28p -20 + 28p + 24p2 = -28p + 28p Combine like terms: -28p + 28p = 0 -20 + 28p + 24p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 7p + 6p2) = 0 Factor a trinomial. 4((-5 + -3p)(1 + -2p)) = 0 Ignore the factor 4.Subproblem 1
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 = -1.666666667Subproblem 2
Set the factor '(1 + -2p)' equal to zero and attempt to solve: Simplifying 1 + -2p = 0 Solving 1 + -2p = 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 + -2p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2p = 0 + -1 -2p = 0 + -1 Combine like terms: 0 + -1 = -1 -2p = -1 Divide each side by '-2'. p = 0.5 Simplifying p = 0.5Solution
p = {-1.666666667, 0.5}
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