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Simplifying 12p2 = -8 + -28p Solving 12p2 = -8 + -28p Solving for variable 'p'. Reorder the terms: 8 + 28p + 12p2 = -8 + -28p + 8 + 28p Reorder the terms: 8 + 28p + 12p2 = -8 + 8 + -28p + 28p Combine like terms: -8 + 8 = 0 8 + 28p + 12p2 = 0 + -28p + 28p 8 + 28p + 12p2 = -28p + 28p Combine like terms: -28p + 28p = 0 8 + 28p + 12p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(2 + 7p + 3p2) = 0 Factor a trinomial. 4((2 + p)(1 + 3p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + p)' equal to zero and attempt to solve: Simplifying 2 + p = 0 Solving 2 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + p = 0 + -2 p = 0 + -2 Combine like terms: 0 + -2 = -2 p = -2 Simplifying p = -2Subproblem 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 = {-2, -0.3333333333}
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