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Simplifying (8p + 6q)(-3p + 12q) = 0 Multiply (8p + 6q) * (-3p + 12q) (8p * (-3p + 12q) + 6q * (-3p + 12q)) = 0 ((-3p * 8p + 12q * 8p) + 6q * (-3p + 12q)) = 0 Reorder the terms: ((96pq + -24p2) + 6q * (-3p + 12q)) = 0 ((96pq + -24p2) + 6q * (-3p + 12q)) = 0 (96pq + -24p2 + (-3p * 6q + 12q * 6q)) = 0 (96pq + -24p2 + (-18pq + 72q2)) = 0 Reorder the terms: (96pq + -18pq + -24p2 + 72q2) = 0 Combine like terms: 96pq + -18pq = 78pq (78pq + -24p2 + 72q2) = 0 Solving 78pq + -24p2 + 72q2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '6'. 6(13pq + -4p2 + 12q2) = 0 Factor a trinomial. 6((-4p + -3q)(p + -4q)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-4p + -3q)' equal to zero and attempt to solve: Simplifying -4p + -3q = 0 Solving -4p + -3q = 0 Move all terms containing p to the left, all other terms to the right. Add '3q' to each side of the equation. -4p + -3q + 3q = 0 + 3q Combine like terms: -3q + 3q = 0 -4p + 0 = 0 + 3q -4p = 0 + 3q Remove the zero: -4p = 3q Divide each side by '-4'. p = -0.75q Simplifying p = -0.75qSubproblem 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 = 4qSolution
p = {-0.75q, 4q}
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