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Simplifying 2(2b + c + -4a) + -7(a + -7c + 9b) = 0 Reorder the terms: 2(-4a + 2b + c) + -7(a + -7c + 9b) = 0 (-4a * 2 + 2b * 2 + c * 2) + -7(a + -7c + 9b) = 0 (-8a + 4b + 2c) + -7(a + -7c + 9b) = 0 Reorder the terms: -8a + 4b + 2c + -7(a + 9b + -7c) = 0 -8a + 4b + 2c + (a * -7 + 9b * -7 + -7c * -7) = 0 -8a + 4b + 2c + (-7a + -63b + 49c) = 0 Reorder the terms: -8a + -7a + 4b + -63b + 2c + 49c = 0 Combine like terms: -8a + -7a = -15a -15a + 4b + -63b + 2c + 49c = 0 Combine like terms: 4b + -63b = -59b -15a + -59b + 2c + 49c = 0 Combine like terms: 2c + 49c = 51c -15a + -59b + 51c = 0 Solving -15a + -59b + 51c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '59b' to each side of the equation. -15a + -59b + 59b + 51c = 0 + 59b Combine like terms: -59b + 59b = 0 -15a + 0 + 51c = 0 + 59b -15a + 51c = 0 + 59b Remove the zero: -15a + 51c = 59b Add '-51c' to each side of the equation. -15a + 51c + -51c = 59b + -51c Combine like terms: 51c + -51c = 0 -15a + 0 = 59b + -51c -15a = 59b + -51c Divide each side by '-15'. a = -3.933333333b + 3.4c Simplifying a = -3.933333333b + 3.4c
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