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Simplifying 8[3a + -4b + c] + 5[2a + -3b + c] + -3[2c + -9a + 7b] = 0 [3a * 8 + -4b * 8 + c * 8] + 5[2a + -3b + c] + -3[2c + -9a + 7b] = 0 [24a + -32b + 8c] + 5[2a + -3b + c] + -3[2c + -9a + 7b] = 0 24a + -32b + 8c + [2a * 5 + -3b * 5 + c * 5] + -3[2c + -9a + 7b] = 0 24a + -32b + 8c + [10a + -15b + 5c] + -3[2c + -9a + 7b] = 0 Reorder the terms: 24a + -32b + 8c + 10a + -15b + 5c + -3[-9a + 7b + 2c] = 0 24a + -32b + 8c + 10a + -15b + 5c + [-9a * -3 + 7b * -3 + 2c * -3] = 0 24a + -32b + 8c + 10a + -15b + 5c + [27a + -21b + -6c] = 0 Reorder the terms: 24a + 10a + 27a + -32b + -15b + -21b + 8c + 5c + -6c = 0 Combine like terms: 24a + 10a = 34a 34a + 27a + -32b + -15b + -21b + 8c + 5c + -6c = 0 Combine like terms: 34a + 27a = 61a 61a + -32b + -15b + -21b + 8c + 5c + -6c = 0 Combine like terms: -32b + -15b = -47b 61a + -47b + -21b + 8c + 5c + -6c = 0 Combine like terms: -47b + -21b = -68b 61a + -68b + 8c + 5c + -6c = 0 Combine like terms: 8c + 5c = 13c 61a + -68b + 13c + -6c = 0 Combine like terms: 13c + -6c = 7c 61a + -68b + 7c = 0 Solving 61a + -68b + 7c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '68b' to each side of the equation. 61a + -68b + 68b + 7c = 0 + 68b Combine like terms: -68b + 68b = 0 61a + 0 + 7c = 0 + 68b 61a + 7c = 0 + 68b Remove the zero: 61a + 7c = 68b Add '-7c' to each side of the equation. 61a + 7c + -7c = 68b + -7c Combine like terms: 7c + -7c = 0 61a + 0 = 68b + -7c 61a = 68b + -7c Divide each side by '61'. a = 1.114754098b + -0.1147540984c Simplifying a = 1.114754098b + -0.1147540984c
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