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Simplifying 30p2 = 12 + -9p Solving 30p2 = 12 + -9p Solving for variable 'p'. Reorder the terms: -12 + 9p + 30p2 = 12 + -9p + -12 + 9p Reorder the terms: -12 + 9p + 30p2 = 12 + -12 + -9p + 9p Combine like terms: 12 + -12 = 0 -12 + 9p + 30p2 = 0 + -9p + 9p -12 + 9p + 30p2 = -9p + 9p Combine like terms: -9p + 9p = 0 -12 + 9p + 30p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 3p + 10p2) = 0 Factor a trinomial. 3((-4 + -5p)(1 + -2p)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -5p)' equal to zero and attempt to solve: Simplifying -4 + -5p = 0 Solving -4 + -5p = 0 Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5p = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5p = 0 + 4 -5p = 0 + 4 Combine like terms: 0 + 4 = 4 -5p = 4 Divide each side by '-5'. p = -0.8 Simplifying p = -0.8Subproblem 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 = {-0.8, 0.5}
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