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Simplifying (12p + 14q) * and(11p + -12q) = 0 Reorder the terms for easier multiplication: adn(12p + 14q)(11p + -12q) = 0 Multiply (12p + 14q) * (11p + -12q) adn(12p * (11p + -12q) + 14q * (11p + -12q)) = 0 adn((11p * 12p + -12q * 12p) + 14q * (11p + -12q)) = 0 Reorder the terms: adn((-144pq + 132p2) + 14q * (11p + -12q)) = 0 adn((-144pq + 132p2) + 14q * (11p + -12q)) = 0 adn(-144pq + 132p2 + (11p * 14q + -12q * 14q)) = 0 adn(-144pq + 132p2 + (154pq + -168q2)) = 0 Reorder the terms: adn(-144pq + 154pq + 132p2 + -168q2) = 0 Combine like terms: -144pq + 154pq = 10pq adn(10pq + 132p2 + -168q2) = 0 (10pq * adn + 132p2 * adn + -168q2 * adn) = 0 (10adnpq + 132adnp2 + -168adnq2) = 0 Solving 10adnpq + 132adnp2 + -168adnq2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '2adn'. 2adn(5pq + 66p2 + -84q2) = 0 Factor a trinomial. 2adn((11p + -12q)(6p + 7q)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'adn' equal to zero and attempt to solve: Simplifying adn = 0 Solving adn = 0 Move all terms containing a to the left, all other terms to the right. Simplifying adn = 0 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 '(11p + -12q)' equal to zero and attempt to solve: Simplifying 11p + -12q = 0 Solving 11p + -12q = 0 Move all terms containing a to the left, all other terms to the right. Add '-11p' to each side of the equation. 11p + -11p + -12q = 0 + -11p Combine like terms: 11p + -11p = 0 0 + -12q = 0 + -11p -12q = 0 + -11p Remove the zero: -12q = -11p Add '12q' to each side of the equation. -12q + 12q = -11p + 12q Combine like terms: -12q + 12q = 0 0 = -11p + 12q Simplifying 0 = -11p + 12q The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(6p + 7q)' equal to zero and attempt to solve: Simplifying 6p + 7q = 0 Solving 6p + 7q = 0 Move all terms containing a to the left, all other terms to the right. Add '-6p' to each side of the equation. 6p + -6p + 7q = 0 + -6p Combine like terms: 6p + -6p = 0 0 + 7q = 0 + -6p 7q = 0 + -6p Remove the zero: 7q = -6p Add '-7q' to each side of the equation. 7q + -7q = -6p + -7q Combine like terms: 7q + -7q = 0 0 = -6p + -7q Simplifying 0 = -6p + -7q The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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