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Simplifying 3(5 + -6a) + 6(a + -1c) = 0 (5 * 3 + -6a * 3) + 6(a + -1c) = 0 (15 + -18a) + 6(a + -1c) = 0 15 + -18a + (a * 6 + -1c * 6) = 0 15 + -18a + (6a + -6c) = 0 Combine like terms: -18a + 6a = -12a 15 + -12a + -6c = 0 Solving 15 + -12a + -6c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -12a + -15 + -6c = 0 + -15 Reorder the terms: 15 + -15 + -12a + -6c = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -12a + -6c = 0 + -15 -12a + -6c = 0 + -15 Combine like terms: 0 + -15 = -15 -12a + -6c = -15 Add '6c' to each side of the equation. -12a + -6c + 6c = -15 + 6c Combine like terms: -6c + 6c = 0 -12a + 0 = -15 + 6c -12a = -15 + 6c Divide each side by '-12'. a = 1.25 + -0.5c Simplifying a = 1.25 + -0.5c
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