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