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Simplifying 4(2b + c + -9a) + -6(a + -7c + 5b) = 0 Reorder the terms: 4(-9a + 2b + c) + -6(a + -7c + 5b) = 0 (-9a * 4 + 2b * 4 + c * 4) + -6(a + -7c + 5b) = 0 (-36a + 8b + 4c) + -6(a + -7c + 5b) = 0 Reorder the terms: -36a + 8b + 4c + -6(a + 5b + -7c) = 0 -36a + 8b + 4c + (a * -6 + 5b * -6 + -7c * -6) = 0 -36a + 8b + 4c + (-6a + -30b + 42c) = 0 Reorder the terms: -36a + -6a + 8b + -30b + 4c + 42c = 0 Combine like terms: -36a + -6a = -42a -42a + 8b + -30b + 4c + 42c = 0 Combine like terms: 8b + -30b = -22b -42a + -22b + 4c + 42c = 0 Combine like terms: 4c + 42c = 46c -42a + -22b + 46c = 0 Solving -42a + -22b + 46c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '22b' to each side of the equation. -42a + -22b + 22b + 46c = 0 + 22b Combine like terms: -22b + 22b = 0 -42a + 0 + 46c = 0 + 22b -42a + 46c = 0 + 22b Remove the zero: -42a + 46c = 22b Add '-46c' to each side of the equation. -42a + 46c + -46c = 22b + -46c Combine like terms: 46c + -46c = 0 -42a + 0 = 22b + -46c -42a = 22b + -46c Divide each side by '-42'. a = -0.5238095238b + 1.095238095c Simplifying a = -0.5238095238b + 1.095238095c
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