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Simplifying p3 + -3p2q + -54pq2 = 0 Reorder the terms: -54pq2 + -3p2q + p3 = 0 Solving -54pq2 + -3p2q + p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(-54q2 + -3pq + p2) = 0 Factor a trinomial. p((-6q + -1p)(9q + -1p)) = 0Subproblem 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 '(-6q + -1p)' equal to zero and attempt to solve: Simplifying -6q + -1p = 0 Reorder the terms: -1p + -6q = 0 Solving -1p + -6q = 0 Move all terms containing p to the left, all other terms to the right. Add '6q' to each side of the equation. -1p + -6q + 6q = 0 + 6q Combine like terms: -6q + 6q = 0 -1p + 0 = 0 + 6q -1p = 0 + 6q Remove the zero: -1p = 6q Divide each side by '-1'. p = -6q Simplifying p = -6qSubproblem 3
Set the factor '(9q + -1p)' equal to zero and attempt to solve: Simplifying 9q + -1p = 0 Reorder the terms: -1p + 9q = 0 Solving -1p + 9q = 0 Move all terms containing p to the left, all other terms to the right. Add '-9q' to each side of the equation. -1p + 9q + -9q = 0 + -9q Combine like terms: 9q + -9q = 0 -1p + 0 = 0 + -9q -1p = 0 + -9q Remove the zero: -1p = -9q Divide each side by '-1'. p = 9q Simplifying p = 9qSolution
p = {0, -6q, 9q}
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