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