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Simplifying 8p4 + 9p2 = (-18p3) Reorder the terms: 9p2 + 8p4 = (-18p3) Solving 9p2 + 8p4 = (-18p3) Solving for variable 'p'. Reorder the terms: 9p2 + (18p3) + 8p4 = (-18p3) + (18p3) Combine like terms: (-18p3) + (18p3) = 0 9p2 + (18p3) + 8p4 = 0 Factor out the Greatest Common Factor (GCF), 'p2'. p2(9 + (18p) + 8p2) = 0 Factor a trinomial. p2((3 + 2p)(3 + 4p)) = 0Subproblem 1
Set the factor 'p2' equal to zero and attempt to solve: Simplifying p2 = 0 Solving p2 = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p2 = 0 Take the square root of each side: p = {0}Subproblem 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 = -1.5Subproblem 3
Set the factor '(3 + 4p)' equal to zero and attempt to solve: Simplifying 3 + 4p = 0 Solving 3 + 4p = 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 + 4p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4p = 0 + -3 4p = 0 + -3 Combine like terms: 0 + -3 = -3 4p = -3 Divide each side by '4'. p = -0.75 Simplifying p = -0.75Solution
p = {0, -1.5, -0.75}
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