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Simplifying 12x + 3(x + 4y) + -12(x + -1y) = 0 12x + (x * 3 + 4y * 3) + -12(x + -1y) = 0 12x + (3x + 12y) + -12(x + -1y) = 0 12x + 3x + 12y + (x * -12 + -1y * -12) = 0 12x + 3x + 12y + (-12x + 12y) = 0 Reorder the terms: 12x + 3x + -12x + 12y + 12y = 0 Combine like terms: 12x + 3x = 15x 15x + -12x + 12y + 12y = 0 Combine like terms: 15x + -12x = 3x 3x + 12y + 12y = 0 Combine like terms: 12y + 12y = 24y 3x + 24y = 0 Solving 3x + 24y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24y' to each side of the equation. 3x + 24y + -24y = 0 + -24y Combine like terms: 24y + -24y = 0 3x + 0 = 0 + -24y 3x = 0 + -24y Remove the zero: 3x = -24y Divide each side by '3'. x = -8y Simplifying x = -8y
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