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Simplifying 3(2a + -2b + c) + -2(a + -3b + c) = 0 (2a * 3 + -2b * 3 + c * 3) + -2(a + -3b + c) = 0 (6a + -6b + 3c) + -2(a + -3b + c) = 0 6a + -6b + 3c + (a * -2 + -3b * -2 + c * -2) = 0 6a + -6b + 3c + (-2a + 6b + -2c) = 0 Reorder the terms: 6a + -2a + -6b + 6b + 3c + -2c = 0 Combine like terms: 6a + -2a = 4a 4a + -6b + 6b + 3c + -2c = 0 Combine like terms: -6b + 6b = 0 4a + 0 + 3c + -2c = 0 4a + 3c + -2c = 0 Combine like terms: 3c + -2c = 1c 4a + 1c = 0 Solving 4a + 1c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1c' to each side of the equation. 4a + 1c + -1c = 0 + -1c Combine like terms: 1c + -1c = 0 4a + 0 = 0 + -1c 4a = 0 + -1c Remove the zero: 4a = -1c Divide each side by '4'. a = -0.25c Simplifying a = -0.25c
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