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Simplifying 12(q + -9) * 8(8p + 6) = 0 Reorder the terms: 12(-9 + q) * 8(8p + 6) = 0 Reorder the terms: 12(-9 + q) * 8(6 + 8p) = 0 Reorder the terms for easier multiplication: 12 * 8(-9 + q)(6 + 8p) = 0 Multiply 12 * 8 96(-9 + q)(6 + 8p) = 0 Multiply (-9 + q) * (6 + 8p) 96(-9(6 + 8p) + q(6 + 8p)) = 0 96((6 * -9 + 8p * -9) + q(6 + 8p)) = 0 96((-54 + -72p) + q(6 + 8p)) = 0 96(-54 + -72p + (6 * q + 8p * q)) = 0 Reorder the terms: 96(-54 + -72p + (8pq + 6q)) = 0 96(-54 + -72p + (8pq + 6q)) = 0 96(-54 + -72p + 8pq + 6q) = 0 (-54 * 96 + -72p * 96 + 8pq * 96 + 6q * 96) = 0 (-5184 + -6912p + 768pq + 576q) = 0 Solving -5184 + -6912p + 768pq + 576q = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5184' to each side of the equation. -5184 + -6912p + 768pq + 5184 + 576q = 0 + 5184 Reorder the terms: -5184 + 5184 + -6912p + 768pq + 576q = 0 + 5184 Combine like terms: -5184 + 5184 = 0 0 + -6912p + 768pq + 576q = 0 + 5184 -6912p + 768pq + 576q = 0 + 5184 Combine like terms: 0 + 5184 = 5184 -6912p + 768pq + 576q = 5184 Add '-576q' to each side of the equation. -6912p + 768pq + 576q + -576q = 5184 + -576q Combine like terms: 576q + -576q = 0 -6912p + 768pq + 0 = 5184 + -576q -6912p + 768pq = 5184 + -576q Reorder the terms: -5184 + -6912p + 768pq + 576q = 5184 + -576q + -5184 + 576q Reorder the terms: -5184 + -6912p + 768pq + 576q = 5184 + -5184 + -576q + 576q Combine like terms: 5184 + -5184 = 0 -5184 + -6912p + 768pq + 576q = 0 + -576q + 576q -5184 + -6912p + 768pq + 576q = -576q + 576q Combine like terms: -576q + 576q = 0 -5184 + -6912p + 768pq + 576q = 0 Factor out the Greatest Common Factor (GCF), '192'. 192(-27 + -36p + 4pq + 3q) = 0 Ignore the factor 192.Subproblem 1
Set the factor '(-27 + -36p + 4pq + 3q)' equal to zero and attempt to solve: Simplifying -27 + -36p + 4pq + 3q = 0 Solving -27 + -36p + 4pq + 3q = 0 Move all terms containing p to the left, all other terms to the right. Add '27' to each side of the equation. -27 + -36p + 4pq + 27 + 3q = 0 + 27 Reorder the terms: -27 + 27 + -36p + 4pq + 3q = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -36p + 4pq + 3q = 0 + 27 -36p + 4pq + 3q = 0 + 27 Combine like terms: 0 + 27 = 27 -36p + 4pq + 3q = 27 Add '-3q' to each side of the equation. -36p + 4pq + 3q + -3q = 27 + -3q Combine like terms: 3q + -3q = 0 -36p + 4pq + 0 = 27 + -3q -36p + 4pq = 27 + -3q 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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