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Simplifying 0 = -40p2 + 20p + 8p + 12 Reorder the terms: 0 = 12 + 20p + 8p + -40p2 Combine like terms: 20p + 8p = 28p 0 = 12 + 28p + -40p2 Solving 0 = 12 + 28p + -40p2 Solving for variable 'p'. Combine like terms: 0 + -12 = -12 -12 + -28p + 40p2 = 12 + 28p + -40p2 + -12 + -28p + 40p2 Reorder the terms: -12 + -28p + 40p2 = 12 + -12 + 28p + -28p + -40p2 + 40p2 Combine like terms: 12 + -12 = 0 -12 + -28p + 40p2 = 0 + 28p + -28p + -40p2 + 40p2 -12 + -28p + 40p2 = 28p + -28p + -40p2 + 40p2 Combine like terms: 28p + -28p = 0 -12 + -28p + 40p2 = 0 + -40p2 + 40p2 -12 + -28p + 40p2 = -40p2 + 40p2 Combine like terms: -40p2 + 40p2 = 0 -12 + -28p + 40p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + -7p + 10p2) = 0 Factor a trinomial. 4((-3 + -10p)(1 + -1p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -10p)' equal to zero and attempt to solve: Simplifying -3 + -10p = 0 Solving -3 + -10p = 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 + -10p = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -10p = 0 + 3 -10p = 0 + 3 Combine like terms: 0 + 3 = 3 -10p = 3 Divide each side by '-10'. p = -0.3 Simplifying p = -0.3Subproblem 2
Set the factor '(1 + -1p)' equal to zero and attempt to solve: Simplifying 1 + -1p = 0 Solving 1 + -1p = 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 + -1p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1p = 0 + -1 -1p = 0 + -1 Combine like terms: 0 + -1 = -1 -1p = -1 Divide each side by '-1'. p = 1 Simplifying p = 1Solution
p = {-0.3, 1}
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