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Simplifying 3(2x + -3y) + 2(3x + 2y) = 0 (2x * 3 + -3y * 3) + 2(3x + 2y) = 0 (6x + -9y) + 2(3x + 2y) = 0 6x + -9y + (3x * 2 + 2y * 2) = 0 6x + -9y + (6x + 4y) = 0 Reorder the terms: 6x + 6x + -9y + 4y = 0 Combine like terms: 6x + 6x = 12x 12x + -9y + 4y = 0 Combine like terms: -9y + 4y = -5y 12x + -5y = 0 Solving 12x + -5y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 12x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 12x + 0 = 0 + 5y 12x = 0 + 5y Remove the zero: 12x = 5y Divide each side by '12'. x = 0.4166666667y Simplifying x = 0.4166666667y
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