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Simplifying 5a + -2b + 3c + 2a + 5b + 4d = 0 Reorder the terms: 5a + 2a + -2b + 5b + 3c + 4d = 0 Combine like terms: 5a + 2a = 7a 7a + -2b + 5b + 3c + 4d = 0 Combine like terms: -2b + 5b = 3b 7a + 3b + 3c + 4d = 0 Solving 7a + 3b + 3c + 4d = 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 + 3c + -3b + 4d = 0 + -3b Reorder the terms: 7a + 3b + -3b + 3c + 4d = 0 + -3b Combine like terms: 3b + -3b = 0 7a + 0 + 3c + 4d = 0 + -3b 7a + 3c + 4d = 0 + -3b Remove the zero: 7a + 3c + 4d = -3b Add '-3c' to each side of the equation. 7a + 3c + -3c + 4d = -3b + -3c Combine like terms: 3c + -3c = 0 7a + 0 + 4d = -3b + -3c 7a + 4d = -3b + -3c Add '-4d' to each side of the equation. 7a + 4d + -4d = -3b + -3c + -4d Combine like terms: 4d + -4d = 0 7a + 0 = -3b + -3c + -4d 7a = -3b + -3c + -4d Divide each side by '7'. a = -0.4285714286b + -0.4285714286c + -0.5714285714d Simplifying a = -0.4285714286b + -0.4285714286c + -0.5714285714d
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