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Simplifying 3(2a + 5c) + -2(4a + -6c) = 0 (2a * 3 + 5c * 3) + -2(4a + -6c) = 0 (6a + 15c) + -2(4a + -6c) = 0 6a + 15c + (4a * -2 + -6c * -2) = 0 6a + 15c + (-8a + 12c) = 0 Reorder the terms: 6a + -8a + 15c + 12c = 0 Combine like terms: 6a + -8a = -2a -2a + 15c + 12c = 0 Combine like terms: 15c + 12c = 27c -2a + 27c = 0 Solving -2a + 27c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-27c' to each side of the equation. -2a + 27c + -27c = 0 + -27c Combine like terms: 27c + -27c = 0 -2a + 0 = 0 + -27c -2a = 0 + -27c Remove the zero: -2a = -27c Divide each side by '-2'. a = 13.5c Simplifying a = 13.5c
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