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Simplifying (m + 2n)(p + 4q) = 0 Multiply (m + 2n) * (p + 4q) (m(p + 4q) + 2n * (p + 4q)) = 0 ((p * m + 4q * m) + 2n * (p + 4q)) = 0 ((mp + 4mq) + 2n * (p + 4q)) = 0 (mp + 4mq + (p * 2n + 4q * 2n)) = 0 (mp + 4mq + (2np + 8nq)) = 0 (mp + 4mq + 2np + 8nq) = 0 Solving mp + 4mq + 2np + 8nq = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2np' to each side of the equation. mp + 4mq + 2np + -2np + 8nq = 0 + -2np Combine like terms: 2np + -2np = 0 mp + 4mq + 0 + 8nq = 0 + -2np mp + 4mq + 8nq = 0 + -2np Remove the zero: mp + 4mq + 8nq = -2np Add '-8nq' to each side of the equation. mp + 4mq + 8nq + -8nq = -2np + -8nq Combine like terms: 8nq + -8nq = 0 mp + 4mq + 0 = -2np + -8nq mp + 4mq = -2np + -8nq Reorder the terms: mp + 4mq + 2np + 8nq = -2np + 2np + -8nq + 8nq Combine like terms: -2np + 2np = 0 mp + 4mq + 2np + 8nq = 0 + -8nq + 8nq mp + 4mq + 2np + 8nq = -8nq + 8nq Combine like terms: -8nq + 8nq = 0 mp + 4mq + 2np + 8nq = 0 The solution to this equation could not be determined.
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