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Simplifying (2p + 5q)(a + 2b + c) = 0 Multiply (2p + 5q) * (a + 2b + c) (2p * (a + 2b + c) + 5q * (a + 2b + c)) = 0 ((a * 2p + 2b * 2p + c * 2p) + 5q * (a + 2b + c)) = 0 ((2ap + 4bp + 2cp) + 5q * (a + 2b + c)) = 0 (2ap + 4bp + 2cp + (a * 5q + 2b * 5q + c * 5q)) = 0 (2ap + 4bp + 2cp + (5aq + 10bq + 5cq)) = 0 Reorder the terms: (2ap + 5aq + 4bp + 10bq + 2cp + 5cq) = 0 (2ap + 5aq + 4bp + 10bq + 2cp + 5cq) = 0 Solving 2ap + 5aq + 4bp + 10bq + 2cp + 5cq = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4bp' to each side of the equation. 2ap + 5aq + 4bp + 10bq + 2cp + -4bp + 5cq = 0 + -4bp Reorder the terms: 2ap + 5aq + 4bp + -4bp + 10bq + 2cp + 5cq = 0 + -4bp Combine like terms: 4bp + -4bp = 0 2ap + 5aq + 0 + 10bq + 2cp + 5cq = 0 + -4bp 2ap + 5aq + 10bq + 2cp + 5cq = 0 + -4bp Remove the zero: 2ap + 5aq + 10bq + 2cp + 5cq = -4bp Add '-10bq' to each side of the equation. 2ap + 5aq + 10bq + 2cp + -10bq + 5cq = -4bp + -10bq Reorder the terms: 2ap + 5aq + 10bq + -10bq + 2cp + 5cq = -4bp + -10bq Combine like terms: 10bq + -10bq = 0 2ap + 5aq + 0 + 2cp + 5cq = -4bp + -10bq 2ap + 5aq + 2cp + 5cq = -4bp + -10bq Add '-2cp' to each side of the equation. 2ap + 5aq + 2cp + -2cp + 5cq = -4bp + -10bq + -2cp Combine like terms: 2cp + -2cp = 0 2ap + 5aq + 0 + 5cq = -4bp + -10bq + -2cp 2ap + 5aq + 5cq = -4bp + -10bq + -2cp Add '-5cq' to each side of the equation. 2ap + 5aq + 5cq + -5cq = -4bp + -10bq + -2cp + -5cq Combine like terms: 5cq + -5cq = 0 2ap + 5aq + 0 = -4bp + -10bq + -2cp + -5cq 2ap + 5aq = -4bp + -10bq + -2cp + -5cq Reorder the terms: 2ap + 5aq + 4bp + 10bq + 2cp + 5cq = -4bp + 4bp + -10bq + 10bq + -2cp + 2cp + -5cq + 5cq Combine like terms: -4bp + 4bp = 0 2ap + 5aq + 4bp + 10bq + 2cp + 5cq = 0 + -10bq + 10bq + -2cp + 2cp + -5cq + 5cq 2ap + 5aq + 4bp + 10bq + 2cp + 5cq = -10bq + 10bq + -2cp + 2cp + -5cq + 5cq Combine like terms: -10bq + 10bq = 0 2ap + 5aq + 4bp + 10bq + 2cp + 5cq = 0 + -2cp + 2cp + -5cq + 5cq 2ap + 5aq + 4bp + 10bq + 2cp + 5cq = -2cp + 2cp + -5cq + 5cq Combine like terms: -2cp + 2cp = 0 2ap + 5aq + 4bp + 10bq + 2cp + 5cq = 0 + -5cq + 5cq 2ap + 5aq + 4bp + 10bq + 2cp + 5cq = -5cq + 5cq Combine like terms: -5cq + 5cq = 0 2ap + 5aq + 4bp + 10bq + 2cp + 5cq = 0 The solution to this equation could not be determined.
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