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Simplifying 5(a + b) + 2(a + c) + -4(b + c) + -4(b + c) = 0 (a * 5 + b * 5) + 2(a + c) + -4(b + c) + -4(b + c) = 0 (5a + 5b) + 2(a + c) + -4(b + c) + -4(b + c) = 0 5a + 5b + (a * 2 + c * 2) + -4(b + c) + -4(b + c) = 0 5a + 5b + (2a + 2c) + -4(b + c) + -4(b + c) = 0 5a + 5b + 2a + 2c + (b * -4 + c * -4) + -4(b + c) = 0 5a + 5b + 2a + 2c + (-4b + -4c) + -4(b + c) = 0 5a + 5b + 2a + 2c + -4b + -4c + (b * -4 + c * -4) = 0 5a + 5b + 2a + 2c + -4b + -4c + (-4b + -4c) = 0 Reorder the terms: 5a + 2a + 5b + -4b + -4b + 2c + -4c + -4c = 0 Combine like terms: 5a + 2a = 7a 7a + 5b + -4b + -4b + 2c + -4c + -4c = 0 Combine like terms: 5b + -4b = 1b 7a + 1b + -4b + 2c + -4c + -4c = 0 Combine like terms: 1b + -4b = -3b 7a + -3b + 2c + -4c + -4c = 0 Combine like terms: 2c + -4c = -2c 7a + -3b + -2c + -4c = 0 Combine like terms: -2c + -4c = -6c 7a + -3b + -6c = 0 Solving 7a + -3b + -6c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 7a + -3b + 3b + -6c = 0 + 3b Combine like terms: -3b + 3b = 0 7a + 0 + -6c = 0 + 3b 7a + -6c = 0 + 3b Remove the zero: 7a + -6c = 3b Add '6c' to each side of the equation. 7a + -6c + 6c = 3b + 6c Combine like terms: -6c + 6c = 0 7a + 0 = 3b + 6c 7a = 3b + 6c Divide each side by '7'. a = 0.4285714286b + 0.8571428571c Simplifying a = 0.4285714286b + 0.8571428571c
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