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Simplifying (a + 2b + 4c + -3d) + -1(3a + -8b + -2c + d) = 0 Remove parenthesis around (a + 2b + 4c + -3d) a + 2b + 4c + -3d + -1(3a + -8b + -2c + d) = 0 a + 2b + 4c + -3d + (3a * -1 + -8b * -1 + -2c * -1 + d * -1) = 0 a + 2b + 4c + -3d + (-3a + 8b + 2c + -1d) = 0 Reorder the terms: a + -3a + 2b + 8b + 4c + 2c + -3d + -1d = 0 Combine like terms: a + -3a = -2a -2a + 2b + 8b + 4c + 2c + -3d + -1d = 0 Combine like terms: 2b + 8b = 10b -2a + 10b + 4c + 2c + -3d + -1d = 0 Combine like terms: 4c + 2c = 6c -2a + 10b + 6c + -3d + -1d = 0 Combine like terms: -3d + -1d = -4d -2a + 10b + 6c + -4d = 0 Solving -2a + 10b + 6c + -4d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10b' to each side of the equation. -2a + 10b + 6c + -10b + -4d = 0 + -10b Reorder the terms: -2a + 10b + -10b + 6c + -4d = 0 + -10b Combine like terms: 10b + -10b = 0 -2a + 0 + 6c + -4d = 0 + -10b -2a + 6c + -4d = 0 + -10b Remove the zero: -2a + 6c + -4d = -10b Add '-6c' to each side of the equation. -2a + 6c + -6c + -4d = -10b + -6c Combine like terms: 6c + -6c = 0 -2a + 0 + -4d = -10b + -6c -2a + -4d = -10b + -6c Add '4d' to each side of the equation. -2a + -4d + 4d = -10b + -6c + 4d Combine like terms: -4d + 4d = 0 -2a + 0 = -10b + -6c + 4d -2a = -10b + -6c + 4d Divide each side by '-2'. a = 5b + 3c + -2d Simplifying a = 5b + 3c + -2d
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