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Simplifying a(p + q) + 2b(p + q) + a(p + -1q) + 2b(p + -1q) = 0 (p * a + q * a) + 2b(p + q) + a(p + -1q) + 2b(p + -1q) = 0 (ap + aq) + 2b(p + q) + a(p + -1q) + 2b(p + -1q) = 0 ap + aq + (p * 2b + q * 2b) + a(p + -1q) + 2b(p + -1q) = 0 ap + aq + (2bp + 2bq) + a(p + -1q) + 2b(p + -1q) = 0 ap + aq + 2bp + 2bq + (p * a + -1q * a) + 2b(p + -1q) = 0 ap + aq + 2bp + 2bq + (ap + -1aq) + 2b(p + -1q) = 0 ap + aq + 2bp + 2bq + ap + -1aq + (p * 2b + -1q * 2b) = 0 ap + aq + 2bp + 2bq + ap + -1aq + (2bp + -2bq) = 0 Reorder the terms: ap + ap + aq + -1aq + 2bp + 2bp + 2bq + -2bq = 0 Combine like terms: ap + ap = 2ap 2ap + aq + -1aq + 2bp + 2bp + 2bq + -2bq = 0 Combine like terms: aq + -1aq = 0 2ap + 0 + 2bp + 2bp + 2bq + -2bq = 0 2ap + 2bp + 2bp + 2bq + -2bq = 0 Combine like terms: 2bp + 2bp = 4bp 2ap + 4bp + 2bq + -2bq = 0 Combine like terms: 2bq + -2bq = 0 2ap + 4bp + 0 = 0 2ap + 4bp = 0 Solving 2ap + 4bp = 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 + 4bp + -4bp = 0 + -4bp Combine like terms: 4bp + -4bp = 0 2ap + 0 = 0 + -4bp 2ap = 0 + -4bp Remove the zero: 2ap = -4bp Divide each side by '2p'. a = -2b Simplifying a = -2b
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