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Simplifying 16p2q + -70pq2 + 24q3 = 0 Reorder the terms: -70pq2 + 16p2q + 24q3 = 0 Solving -70pq2 + 16p2q + 24q3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2q'. 2q(-35pq + 8p2 + 12q2) = 0 Factor a trinomial. 2q((p + -4q)(8p + -3q)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'q' equal to zero and attempt to solve: Simplifying q = 0 Solving q = 0 Move all terms containing p to the left, all other terms to the right. Add '-1q' to each side of the equation. q + -1q = 0 + -1q Remove the zero: 0 = -1q Simplifying 0 = -1q The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(p + -4q)' equal to zero and attempt to solve: Simplifying p + -4q = 0 Solving p + -4q = 0 Move all terms containing p to the left, all other terms to the right. Add '4q' to each side of the equation. p + -4q + 4q = 0 + 4q Combine like terms: -4q + 4q = 0 p + 0 = 0 + 4q p = 0 + 4q Remove the zero: p = 4q Simplifying p = 4qSubproblem 3
Set the factor '(8p + -3q)' equal to zero and attempt to solve: Simplifying 8p + -3q = 0 Solving 8p + -3q = 0 Move all terms containing p to the left, all other terms to the right. Add '3q' to each side of the equation. 8p + -3q + 3q = 0 + 3q Combine like terms: -3q + 3q = 0 8p + 0 = 0 + 3q 8p = 0 + 3q Remove the zero: 8p = 3q Divide each side by '8'. p = 0.375q Simplifying p = 0.375qSolution
p = {4q, 0.375q}
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