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Simplifying p3 + p2q + -56pq2 = 0 Reorder the terms: -56pq2 + p2q + p3 = 0 Solving -56pq2 + p2q + p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(-56q2 + pq + p2) = 0 Factor a trinomial. p((-8q + -1p)(7q + -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 '(-8q + -1p)' equal to zero and attempt to solve: Simplifying -8q + -1p = 0 Reorder the terms: -1p + -8q = 0 Solving -1p + -8q = 0 Move all terms containing p to the left, all other terms to the right. Add '8q' to each side of the equation. -1p + -8q + 8q = 0 + 8q Combine like terms: -8q + 8q = 0 -1p + 0 = 0 + 8q -1p = 0 + 8q Remove the zero: -1p = 8q Divide each side by '-1'. p = -8q Simplifying p = -8qSubproblem 3
Set the factor '(7q + -1p)' equal to zero and attempt to solve: Simplifying 7q + -1p = 0 Reorder the terms: -1p + 7q = 0 Solving -1p + 7q = 0 Move all terms containing p to the left, all other terms to the right. Add '-7q' to each side of the equation. -1p + 7q + -7q = 0 + -7q Combine like terms: 7q + -7q = 0 -1p + 0 = 0 + -7q -1p = 0 + -7q Remove the zero: -1p = -7q Divide each side by '-1'. p = 7q Simplifying p = 7qSolution
p = {0, -8q, 7q}
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