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Simplifying 5(2a + -1c) + 4(3a + 2c) = 0 (2a * 5 + -1c * 5) + 4(3a + 2c) = 0 (10a + -5c) + 4(3a + 2c) = 0 10a + -5c + (3a * 4 + 2c * 4) = 0 10a + -5c + (12a + 8c) = 0 Reorder the terms: 10a + 12a + -5c + 8c = 0 Combine like terms: 10a + 12a = 22a 22a + -5c + 8c = 0 Combine like terms: -5c + 8c = 3c 22a + 3c = 0 Solving 22a + 3c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3c' to each side of the equation. 22a + 3c + -3c = 0 + -3c Combine like terms: 3c + -3c = 0 22a + 0 = 0 + -3c 22a = 0 + -3c Remove the zero: 22a = -3c Divide each side by '22'. a = -0.1363636364c Simplifying a = -0.1363636364c
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