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Simplifying 6(7b + c + -5a) + -9(9 + -3c + 6b) = 0 Reorder the terms: 6(-5a + 7b + c) + -9(9 + -3c + 6b) = 0 (-5a * 6 + 7b * 6 + c * 6) + -9(9 + -3c + 6b) = 0 (-30a + 42b + 6c) + -9(9 + -3c + 6b) = 0 Reorder the terms: -30a + 42b + 6c + -9(9 + 6b + -3c) = 0 -30a + 42b + 6c + (9 * -9 + 6b * -9 + -3c * -9) = 0 -30a + 42b + 6c + (-81 + -54b + 27c) = 0 Reorder the terms: -81 + -30a + 42b + -54b + 6c + 27c = 0 Combine like terms: 42b + -54b = -12b -81 + -30a + -12b + 6c + 27c = 0 Combine like terms: 6c + 27c = 33c -81 + -30a + -12b + 33c = 0 Solving -81 + -30a + -12b + 33c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '81' to each side of the equation. -81 + -30a + -12b + 81 + 33c = 0 + 81 Reorder the terms: -81 + 81 + -30a + -12b + 33c = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -30a + -12b + 33c = 0 + 81 -30a + -12b + 33c = 0 + 81 Combine like terms: 0 + 81 = 81 -30a + -12b + 33c = 81 Add '12b' to each side of the equation. -30a + -12b + 12b + 33c = 81 + 12b Combine like terms: -12b + 12b = 0 -30a + 0 + 33c = 81 + 12b -30a + 33c = 81 + 12b Add '-33c' to each side of the equation. -30a + 33c + -33c = 81 + 12b + -33c Combine like terms: 33c + -33c = 0 -30a + 0 = 81 + 12b + -33c -30a = 81 + 12b + -33c Divide each side by '-30'. a = -2.7 + -0.4b + 1.1c Simplifying a = -2.7 + -0.4b + 1.1c
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