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Simplifying 12a + 19b + 6c + 4c + -3b + -4a = 0 Reorder the terms: 12a + -4a + 19b + -3b + 6c + 4c = 0 Combine like terms: 12a + -4a = 8a 8a + 19b + -3b + 6c + 4c = 0 Combine like terms: 19b + -3b = 16b 8a + 16b + 6c + 4c = 0 Combine like terms: 6c + 4c = 10c 8a + 16b + 10c = 0 Solving 8a + 16b + 10c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-16b' to each side of the equation. 8a + 16b + -16b + 10c = 0 + -16b Combine like terms: 16b + -16b = 0 8a + 0 + 10c = 0 + -16b 8a + 10c = 0 + -16b Remove the zero: 8a + 10c = -16b Add '-10c' to each side of the equation. 8a + 10c + -10c = -16b + -10c Combine like terms: 10c + -10c = 0 8a + 0 = -16b + -10c 8a = -16b + -10c Divide each side by '8'. a = -2b + -1.25c Simplifying a = -2b + -1.25c
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