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Simplifying 32p3 + -2pq2 = 0 Reorder the terms: -2pq2 + 32p3 = 0 Solving -2pq2 + 32p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2p'. 2p(-1q2 + 16p2) = 0 Factor a difference between two squares. 2p((q + 4p)(-1q + 4p)) = 0 Ignore the factor 2.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 '(q + 4p)' equal to zero and attempt to solve: Simplifying q + 4p = 0 Reorder the terms: 4p + q = 0 Solving 4p + q = 0 Move all terms containing p to the left, all other terms to the right. Add '-1q' to each side of the equation. 4p + q + -1q = 0 + -1q Combine like terms: q + -1q = 0 4p + 0 = 0 + -1q 4p = 0 + -1q Remove the zero: 4p = -1q Divide each side by '4'. p = -0.25q Simplifying p = -0.25qSubproblem 3
Set the factor '(-1q + 4p)' equal to zero and attempt to solve: Simplifying -1q + 4p = 0 Reorder the terms: 4p + -1q = 0 Solving 4p + -1q = 0 Move all terms containing p to the left, all other terms to the right. Add 'q' to each side of the equation. 4p + -1q + q = 0 + q Combine like terms: -1q + q = 0 4p + 0 = 0 + q 4p = 0 + q Remove the zero: 4p = q Divide each side by '4'. p = 0.25q Simplifying p = 0.25qSolution
p = {0, -0.25q, 0.25q}
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