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Simplifying 5(2a + -1c) + 3(3a + 2c) = 0 (2a * 5 + -1c * 5) + 3(3a + 2c) = 0 (10a + -5c) + 3(3a + 2c) = 0 10a + -5c + (3a * 3 + 2c * 3) = 0 10a + -5c + (9a + 6c) = 0 Reorder the terms: 10a + 9a + -5c + 6c = 0 Combine like terms: 10a + 9a = 19a 19a + -5c + 6c = 0 Combine like terms: -5c + 6c = 1c 19a + 1c = 0 Solving 19a + 1c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1c' to each side of the equation. 19a + 1c + -1c = 0 + -1c Combine like terms: 1c + -1c = 0 19a + 0 = 0 + -1c 19a = 0 + -1c Remove the zero: 19a = -1c Divide each side by '19'. a = -0.05263157895c Simplifying a = -0.05263157895c
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