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Simplifying (3m + -5)(q + 4) * 2p(4 + -6n) = 0 Reorder the terms: (-5 + 3m)(q + 4) * 2p(4 + -6n) = 0 Reorder the terms: (-5 + 3m)(4 + q) * 2p(4 + -6n) = 0 Reorder the terms for easier multiplication: 2p(-5 + 3m)(4 + q)(4 + -6n) = 0 Multiply (-5 + 3m) * (4 + q) 2p(-5(4 + q) + 3m * (4 + q))(4 + -6n) = 0 2p((4 * -5 + q * -5) + 3m * (4 + q))(4 + -6n) = 0 2p((-20 + -5q) + 3m * (4 + q))(4 + -6n) = 0 2p(-20 + -5q + (4 * 3m + q * 3m))(4 + -6n) = 0 2p(-20 + -5q + (12m + 3mq))(4 + -6n) = 0 Reorder the terms: 2p(-20 + 12m + 3mq + -5q)(4 + -6n) = 0 2p(-20 + 12m + 3mq + -5q)(4 + -6n) = 0 Multiply (-20 + 12m + 3mq + -5q) * (4 + -6n) 2p(-20(4 + -6n) + 12m * (4 + -6n) + 3mq * (4 + -6n) + -5q * (4 + -6n)) = 0 2p((4 * -20 + -6n * -20) + 12m * (4 + -6n) + 3mq * (4 + -6n) + -5q * (4 + -6n)) = 0 2p((-80 + 120n) + 12m * (4 + -6n) + 3mq * (4 + -6n) + -5q * (4 + -6n)) = 0 2p(-80 + 120n + (4 * 12m + -6n * 12m) + 3mq * (4 + -6n) + -5q * (4 + -6n)) = 0 2p(-80 + 120n + (48m + -72mn) + 3mq * (4 + -6n) + -5q * (4 + -6n)) = 0 2p(-80 + 120n + 48m + -72mn + (4 * 3mq + -6n * 3mq) + -5q * (4 + -6n)) = 0 Reorder the terms: 2p(-80 + 120n + 48m + -72mn + (-18mnq + 12mq) + -5q * (4 + -6n)) = 0 2p(-80 + 120n + 48m + -72mn + (-18mnq + 12mq) + -5q * (4 + -6n)) = 0 2p(-80 + 120n + 48m + -72mn + -18mnq + 12mq + (4 * -5q + -6n * -5q)) = 0 Reorder the terms: 2p(-80 + 120n + 48m + -72mn + -18mnq + 12mq + (30nq + -20q)) = 0 2p(-80 + 120n + 48m + -72mn + -18mnq + 12mq + (30nq + -20q)) = 0 Reorder the terms: 2p(-80 + 48m + -72mn + -18mnq + 12mq + 120n + 30nq + -20q) = 0 2p(-80 + 48m + -72mn + -18mnq + 12mq + 120n + 30nq + -20q) = 0 (-80 * 2p + 48m * 2p + -72mn * 2p + -18mnq * 2p + 12mq * 2p + 120n * 2p + 30nq * 2p + -20q * 2p) = 0 Reorder the terms: (-144mnp + -36mnpq + 96mp + 24mpq + 240np + 60npq + -160p + -40pq) = 0 (-144mnp + -36mnpq + 96mp + 24mpq + 240np + 60npq + -160p + -40pq) = 0 Solving -144mnp + -36mnpq + 96mp + 24mpq + 240np + 60npq + -160p + -40pq = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-240np' to each side of the equation. -144mnp + -36mnpq + 96mp + 24mpq + 240np + 60npq + -160p + -240np + -40pq = 0 + -240np Reorder the terms: -144mnp + -36mnpq + 96mp + 24mpq + 240np + -240np + 60npq + -160p + -40pq = 0 + -240np Combine like terms: 240np + -240np = 0 -144mnp + -36mnpq + 96mp + 24mpq + 0 + 60npq + -160p + -40pq = 0 + -240np -144mnp + -36mnpq + 96mp + 24mpq + 60npq + -160p + -40pq = 0 + -240np Remove the zero: -144mnp + -36mnpq + 96mp + 24mpq + 60npq + -160p + -40pq = -240np Add '-60npq' to each side of the equation. -144mnp + -36mnpq + 96mp + 24mpq + 60npq + -160p + -60npq + -40pq = -240np + -60npq Reorder the terms: -144mnp + -36mnpq + 96mp + 24mpq + 60npq + -60npq + -160p + -40pq = -240np + -60npq Combine like terms: 60npq + -60npq = 0 -144mnp + -36mnpq + 96mp + 24mpq + 0 + -160p + -40pq = -240np + -60npq -144mnp + -36mnpq + 96mp + 24mpq + -160p + -40pq = -240np + -60npq Add '160p' to each side of the equation. -144mnp + -36mnpq + 96mp + 24mpq + -160p + 160p + -40pq = -240np + -60npq + 160p Combine like terms: -160p + 160p = 0 -144mnp + -36mnpq + 96mp + 24mpq + 0 + -40pq = -240np + -60npq + 160p -144mnp + -36mnpq + 96mp + 24mpq + -40pq = -240np + -60npq + 160p Add '40pq' to each side of the equation. -144mnp + -36mnpq + 96mp + 24mpq + -40pq + 40pq = -240np + -60npq + 160p + 40pq Combine like terms: -40pq + 40pq = 0 -144mnp + -36mnpq + 96mp + 24mpq + 0 = -240np + -60npq + 160p + 40pq -144mnp + -36mnpq + 96mp + 24mpq = -240np + -60npq + 160p + 40pq Reorder the terms: -144mnp + -36mnpq + 96mp + 24mpq + 240np + 60npq + -160p + -40pq = -240np + 240np + -60npq + 60npq + 160p + -160p + 40pq + -40pq Combine like terms: -240np + 240np = 0 -144mnp + -36mnpq + 96mp + 24mpq + 240np + 60npq + -160p + -40pq = 0 + -60npq + 60npq + 160p + -160p + 40pq + -40pq -144mnp + -36mnpq + 96mp + 24mpq + 240np + 60npq + -160p + -40pq = -60npq + 60npq + 160p + -160p + 40pq + -40pq Combine like terms: -60npq + 60npq = 0 -144mnp + -36mnpq + 96mp + 24mpq + 240np + 60npq + -160p + -40pq = 0 + 160p + -160p + 40pq + -40pq -144mnp + -36mnpq + 96mp + 24mpq + 240np + 60npq + -160p + -40pq = 160p + -160p + 40pq + -40pq Combine like terms: 160p + -160p = 0 -144mnp + -36mnpq + 96mp + 24mpq + 240np + 60npq + -160p + -40pq = 0 + 40pq + -40pq -144mnp + -36mnpq + 96mp + 24mpq + 240np + 60npq + -160p + -40pq = 40pq + -40pq Combine like terms: 40pq + -40pq = 0 -144mnp + -36mnpq + 96mp + 24mpq + 240np + 60npq + -160p + -40pq = 0 Factor out the Greatest Common Factor (GCF), '4p'. 4p(-36mn + -9mnq + 24m + 6mq + 60n + 15nq + -40 + -10q) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing m to the left, all other terms to the right. Add '-1p' to each side of the equation. p + -1p = 0 + -1p Remove the zero: 0 = -1p Simplifying 0 = -1p 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 '(-36mn + -9mnq + 24m + 6mq + 60n + 15nq + -40 + -10q)' equal to zero and attempt to solve: Simplifying -36mn + -9mnq + 24m + 6mq + 60n + 15nq + -40 + -10q = 0 Reorder the terms: -40 + 24m + -36mn + -9mnq + 6mq + 60n + 15nq + -10q = 0 Solving -40 + 24m + -36mn + -9mnq + 6mq + 60n + 15nq + -10q = 0 Move all terms containing m to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 24m + -36mn + -9mnq + 6mq + 60n + 15nq + 40 + -10q = 0 + 40 Reorder the terms: -40 + 40 + 24m + -36mn + -9mnq + 6mq + 60n + 15nq + -10q = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 24m + -36mn + -9mnq + 6mq + 60n + 15nq + -10q = 0 + 40 24m + -36mn + -9mnq + 6mq + 60n + 15nq + -10q = 0 + 40 Combine like terms: 0 + 40 = 40 24m + -36mn + -9mnq + 6mq + 60n + 15nq + -10q = 40 Add '-60n' to each side of the equation. 24m + -36mn + -9mnq + 6mq + 60n + 15nq + -60n + -10q = 40 + -60n Reorder the terms: 24m + -36mn + -9mnq + 6mq + 60n + -60n + 15nq + -10q = 40 + -60n Combine like terms: 60n + -60n = 0 24m + -36mn + -9mnq + 6mq + 0 + 15nq + -10q = 40 + -60n 24m + -36mn + -9mnq + 6mq + 15nq + -10q = 40 + -60n Add '-15nq' to each side of the equation. 24m + -36mn + -9mnq + 6mq + 15nq + -15nq + -10q = 40 + -60n + -15nq Combine like terms: 15nq + -15nq = 0 24m + -36mn + -9mnq + 6mq + 0 + -10q = 40 + -60n + -15nq 24m + -36mn + -9mnq + 6mq + -10q = 40 + -60n + -15nq Add '10q' to each side of the equation. 24m + -36mn + -9mnq + 6mq + -10q + 10q = 40 + -60n + -15nq + 10q Combine like terms: -10q + 10q = 0 24m + -36mn + -9mnq + 6mq + 0 = 40 + -60n + -15nq + 10q 24m + -36mn + -9mnq + 6mq = 40 + -60n + -15nq + 10q 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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