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Simplifying (4p2q + -1pq2 + q3) + -1(3p2q + 2pq2 + -1q3) = 0 Reorder the terms: (-1pq2 + 4p2q + q3) + -1(3p2q + 2pq2 + -1q3) = 0 Remove parenthesis around (-1pq2 + 4p2q + q3) -1pq2 + 4p2q + q3 + -1(3p2q + 2pq2 + -1q3) = 0 Reorder the terms: -1pq2 + 4p2q + q3 + -1(2pq2 + 3p2q + -1q3) = 0 -1pq2 + 4p2q + q3 + (2pq2 * -1 + 3p2q * -1 + -1q3 * -1) = 0 -1pq2 + 4p2q + q3 + (-2pq2 + -3p2q + 1q3) = 0 Reorder the terms: -1pq2 + -2pq2 + 4p2q + -3p2q + q3 + 1q3 = 0 Combine like terms: -1pq2 + -2pq2 = -3pq2 -3pq2 + 4p2q + -3p2q + q3 + 1q3 = 0 Combine like terms: 4p2q + -3p2q = 1p2q -3pq2 + 1p2q + q3 + 1q3 = 0 Combine like terms: q3 + 1q3 = 2q3 -3pq2 + 1p2q + 2q3 = 0 Solving -3pq2 + 1p2q + 2q3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'q'. q(-3pq + p2 + 2q2) = 0 Factor a trinomial. q((p + -2q)(p + -1q)) = 0Subproblem 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 + -2q)' equal to zero and attempt to solve: Simplifying p + -2q = 0 Solving p + -2q = 0 Move all terms containing p to the left, all other terms to the right. Add '2q' to each side of the equation. p + -2q + 2q = 0 + 2q Combine like terms: -2q + 2q = 0 p + 0 = 0 + 2q p = 0 + 2q Remove the zero: p = 2q Simplifying p = 2qSubproblem 3
Set the factor '(p + -1q)' equal to zero and attempt to solve: Simplifying p + -1q = 0 Solving p + -1q = 0 Move all terms containing p to the left, all other terms to the right. Add 'q' to each side of the equation. p + -1q + q = 0 + q Combine like terms: -1q + q = 0 p + 0 = 0 + q p = 0 + q Remove the zero: p = q Simplifying p = qSolution
p = {2q, q}
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