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Simplifying 6(3 + -1a) + 7(3a + 2) + -4(a + 5) = 0 (3 * 6 + -1a * 6) + 7(3a + 2) + -4(a + 5) = 0 (18 + -6a) + 7(3a + 2) + -4(a + 5) = 0 Reorder the terms: 18 + -6a + 7(2 + 3a) + -4(a + 5) = 0 18 + -6a + (2 * 7 + 3a * 7) + -4(a + 5) = 0 18 + -6a + (14 + 21a) + -4(a + 5) = 0 Reorder the terms: 18 + -6a + 14 + 21a + -4(5 + a) = 0 18 + -6a + 14 + 21a + (5 * -4 + a * -4) = 0 18 + -6a + 14 + 21a + (-20 + -4a) = 0 Reorder the terms: 18 + 14 + -20 + -6a + 21a + -4a = 0 Combine like terms: 18 + 14 = 32 32 + -20 + -6a + 21a + -4a = 0 Combine like terms: 32 + -20 = 12 12 + -6a + 21a + -4a = 0 Combine like terms: -6a + 21a = 15a 12 + 15a + -4a = 0 Combine like terms: 15a + -4a = 11a 12 + 11a = 0 Solving 12 + 11a = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + 11a = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 11a = 0 + -12 11a = 0 + -12 Combine like terms: 0 + -12 = -12 11a = -12 Divide each side by '11'. a = -1.090909091 Simplifying a = -1.090909091
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