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Simplifying (2z + 5c + -3a) + -1(6a + 2c + -4z) = 0 Reorder the terms: (-3a + 5c + 2z) + -1(6a + 2c + -4z) = 0 Remove parenthesis around (-3a + 5c + 2z) -3a + 5c + 2z + -1(6a + 2c + -4z) = 0 -3a + 5c + 2z + (6a * -1 + 2c * -1 + -4z * -1) = 0 -3a + 5c + 2z + (-6a + -2c + 4z) = 0 Reorder the terms: -3a + -6a + 5c + -2c + 2z + 4z = 0 Combine like terms: -3a + -6a = -9a -9a + 5c + -2c + 2z + 4z = 0 Combine like terms: 5c + -2c = 3c -9a + 3c + 2z + 4z = 0 Combine like terms: 2z + 4z = 6z -9a + 3c + 6z = 0 Solving -9a + 3c + 6z = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3c' to each side of the equation. -9a + 3c + -3c + 6z = 0 + -3c Combine like terms: 3c + -3c = 0 -9a + 0 + 6z = 0 + -3c -9a + 6z = 0 + -3c Remove the zero: -9a + 6z = -3c Add '-6z' to each side of the equation. -9a + 6z + -6z = -3c + -6z Combine like terms: 6z + -6z = 0 -9a + 0 = -3c + -6z -9a = -3c + -6z Divide each side by '-9'. a = 0.3333333333c + 0.6666666667z Simplifying a = 0.3333333333c + 0.6666666667z
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