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Simplifying 2(3a + 4c + -5d) = 0 (3a * 2 + 4c * 2 + -5d * 2) = 0 (6a + 8c + -10d) = 0 Solving 6a + 8c + -10d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8c' to each side of the equation. 6a + 8c + -8c + -10d = 0 + -8c Combine like terms: 8c + -8c = 0 6a + 0 + -10d = 0 + -8c 6a + -10d = 0 + -8c Remove the zero: 6a + -10d = -8c Add '10d' to each side of the equation. 6a + -10d + 10d = -8c + 10d Combine like terms: -10d + 10d = 0 6a + 0 = -8c + 10d 6a = -8c + 10d Divide each side by '6'. a = -1.333333333c + 1.666666667d Simplifying a = -1.333333333c + 1.666666667d
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