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Simplifying -4p2 = 18p + 18 Reorder the terms: -4p2 = 18 + 18p Solving -4p2 = 18 + 18p Solving for variable 'p'. Reorder the terms: -18 + -18p + -4p2 = 18 + 18p + -18 + -18p Reorder the terms: -18 + -18p + -4p2 = 18 + -18 + 18p + -18p Combine like terms: 18 + -18 = 0 -18 + -18p + -4p2 = 0 + 18p + -18p -18 + -18p + -4p2 = 18p + -18p Combine like terms: 18p + -18p = 0 -18 + -18p + -4p2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(9 + 9p + 2p2) = 0 Factor a trinomial. -2((3 + p)(3 + 2p)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(3 + p)' equal to zero and attempt to solve: Simplifying 3 + p = 0 Solving 3 + p = 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 + p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + p = 0 + -3 p = 0 + -3 Combine like terms: 0 + -3 = -3 p = -3 Simplifying p = -3Subproblem 2
Set the factor '(3 + 2p)' equal to zero and attempt to solve: Simplifying 3 + 2p = 0 Solving 3 + 2p = 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 + 2p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2p = 0 + -3 2p = 0 + -3 Combine like terms: 0 + -3 = -3 2p = -3 Divide each side by '2'. p = -1.5 Simplifying p = -1.5Solution
p = {-3, -1.5}
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