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Simplifying (-6a + 8b + -1c) + -1(-2b + 4c + -6d) = 0 Remove parenthesis around (-6a + 8b + -1c) -6a + 8b + -1c + -1(-2b + 4c + -6d) = 0 -6a + 8b + -1c + (-2b * -1 + 4c * -1 + -6d * -1) = 0 -6a + 8b + -1c + (2b + -4c + 6d) = 0 Reorder the terms: -6a + 8b + 2b + -1c + -4c + 6d = 0 Combine like terms: 8b + 2b = 10b -6a + 10b + -1c + -4c + 6d = 0 Combine like terms: -1c + -4c = -5c -6a + 10b + -5c + 6d = 0 Solving -6a + 10b + -5c + 6d = 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. -6a + 10b + -5c + -10b + 6d = 0 + -10b Reorder the terms: -6a + 10b + -10b + -5c + 6d = 0 + -10b Combine like terms: 10b + -10b = 0 -6a + 0 + -5c + 6d = 0 + -10b -6a + -5c + 6d = 0 + -10b Remove the zero: -6a + -5c + 6d = -10b Add '5c' to each side of the equation. -6a + -5c + 5c + 6d = -10b + 5c Combine like terms: -5c + 5c = 0 -6a + 0 + 6d = -10b + 5c -6a + 6d = -10b + 5c Add '-6d' to each side of the equation. -6a + 6d + -6d = -10b + 5c + -6d Combine like terms: 6d + -6d = 0 -6a + 0 = -10b + 5c + -6d -6a = -10b + 5c + -6d Divide each side by '-6'. a = 1.666666667b + -0.8333333333c + d Simplifying a = 1.666666667b + -0.8333333333c + d
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