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Simplifying 24p2 + -12p = 24p + -12p3 Reorder the terms: -12p + 24p2 = 24p + -12p3 Solving -12p + 24p2 = 24p + -12p3 Solving for variable 'p'. Reorder the terms: -12p + -24p + 24p2 + 12p3 = 24p + -12p3 + -24p + 12p3 Combine like terms: -12p + -24p = -36p -36p + 24p2 + 12p3 = 24p + -12p3 + -24p + 12p3 Reorder the terms: -36p + 24p2 + 12p3 = 24p + -24p + -12p3 + 12p3 Combine like terms: 24p + -24p = 0 -36p + 24p2 + 12p3 = 0 + -12p3 + 12p3 -36p + 24p2 + 12p3 = -12p3 + 12p3 Combine like terms: -12p3 + 12p3 = 0 -36p + 24p2 + 12p3 = 0 Factor out the Greatest Common Factor (GCF), '12p'. 12p(-3 + 2p + p2) = 0 Factor a trinomial. 12p((-3 + -1p)(1 + -1p)) = 0 Ignore the factor 12.Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 2
Set the factor '(-3 + -1p)' equal to zero and attempt to solve: Simplifying -3 + -1p = 0 Solving -3 + -1p = 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 + -1p = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1p = 0 + 3 -1p = 0 + 3 Combine like terms: 0 + 3 = 3 -1p = 3 Divide each side by '-1'. p = -3 Simplifying p = -3Subproblem 3
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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