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Simplifying 9(2a + 4b + -7c) + -4(b + -1c) + -7(-1c + -4b) = 0 (2a * 9 + 4b * 9 + -7c * 9) + -4(b + -1c) + -7(-1c + -4b) = 0 (18a + 36b + -63c) + -4(b + -1c) + -7(-1c + -4b) = 0 18a + 36b + -63c + (b * -4 + -1c * -4) + -7(-1c + -4b) = 0 18a + 36b + -63c + (-4b + 4c) + -7(-1c + -4b) = 0 Reorder the terms: 18a + 36b + -63c + -4b + 4c + -7(-4b + -1c) = 0 18a + 36b + -63c + -4b + 4c + (-4b * -7 + -1c * -7) = 0 18a + 36b + -63c + -4b + 4c + (28b + 7c) = 0 Reorder the terms: 18a + 36b + -4b + 28b + -63c + 4c + 7c = 0 Combine like terms: 36b + -4b = 32b 18a + 32b + 28b + -63c + 4c + 7c = 0 Combine like terms: 32b + 28b = 60b 18a + 60b + -63c + 4c + 7c = 0 Combine like terms: -63c + 4c = -59c 18a + 60b + -59c + 7c = 0 Combine like terms: -59c + 7c = -52c 18a + 60b + -52c = 0 Solving 18a + 60b + -52c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-60b' to each side of the equation. 18a + 60b + -60b + -52c = 0 + -60b Combine like terms: 60b + -60b = 0 18a + 0 + -52c = 0 + -60b 18a + -52c = 0 + -60b Remove the zero: 18a + -52c = -60b Add '52c' to each side of the equation. 18a + -52c + 52c = -60b + 52c Combine like terms: -52c + 52c = 0 18a + 0 = -60b + 52c 18a = -60b + 52c Divide each side by '18'. a = -3.333333333b + 2.888888889c Simplifying a = -3.333333333b + 2.888888889c
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