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Simplifying A(2p + -1q) + -1q(2p + -3a) = 0 (2p * A + -1q * A) + -1q(2p + -3a) = 0 (2pA + -1qA) + -1q(2p + -3a) = 0 Reorder the terms: 2pA + -1qA + -1q(-3a + 2p) = 0 2pA + -1qA + (-3a * -1q + 2p * -1q) = 0 2pA + -1qA + (3aq + -2pq) = 0 Reorder the terms: 3aq + 2pA + -2pq + -1qA = 0 Solving 3aq + 2pA + -2pq + -1qA = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2pA' to each side of the equation. 3aq + 2pA + -2pq + -2pA + -1qA = 0 + -2pA Reorder the terms: 3aq + 2pA + -2pA + -2pq + -1qA = 0 + -2pA Combine like terms: 2pA + -2pA = 0 3aq + 0 + -2pq + -1qA = 0 + -2pA 3aq + -2pq + -1qA = 0 + -2pA Remove the zero: 3aq + -2pq + -1qA = -2pA Add '2pq' to each side of the equation. 3aq + -2pq + 2pq + -1qA = -2pA + 2pq Combine like terms: -2pq + 2pq = 0 3aq + 0 + -1qA = -2pA + 2pq 3aq + -1qA = -2pA + 2pq Add 'qA' to each side of the equation. 3aq + -1qA + qA = -2pA + 2pq + qA Combine like terms: -1qA + qA = 0 3aq + 0 = -2pA + 2pq + qA 3aq = -2pA + 2pq + qA Divide each side by '3q'. a = -0.6666666667pq-1A + 0.6666666667p + 0.3333333333A Simplifying a = -0.6666666667pq-1A + 0.6666666667p + 0.3333333333A Reorder the terms: a = 0.3333333333A + 0.6666666667p + -0.6666666667pq-1A
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