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Simplifying 3(p + q + 7) + 4(2p + 4q + 6) = 0 Reorder the terms: 3(7 + p + q) + 4(2p + 4q + 6) = 0 (7 * 3 + p * 3 + q * 3) + 4(2p + 4q + 6) = 0 (21 + 3p + 3q) + 4(2p + 4q + 6) = 0 Reorder the terms: 21 + 3p + 3q + 4(6 + 2p + 4q) = 0 21 + 3p + 3q + (6 * 4 + 2p * 4 + 4q * 4) = 0 21 + 3p + 3q + (24 + 8p + 16q) = 0 Reorder the terms: 21 + 24 + 3p + 8p + 3q + 16q = 0 Combine like terms: 21 + 24 = 45 45 + 3p + 8p + 3q + 16q = 0 Combine like terms: 3p + 8p = 11p 45 + 11p + 3q + 16q = 0 Combine like terms: 3q + 16q = 19q 45 + 11p + 19q = 0 Solving 45 + 11p + 19q = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + 11p + -45 + 19q = 0 + -45 Reorder the terms: 45 + -45 + 11p + 19q = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 11p + 19q = 0 + -45 11p + 19q = 0 + -45 Combine like terms: 0 + -45 = -45 11p + 19q = -45 Add '-19q' to each side of the equation. 11p + 19q + -19q = -45 + -19q Combine like terms: 19q + -19q = 0 11p + 0 = -45 + -19q 11p = -45 + -19q Divide each side by '11'. p = -4.090909091 + -1.727272727q Simplifying p = -4.090909091 + -1.727272727q
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