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Simplifying 2(2x + 3y) + 3(4x + 2y) = 0 (2x * 2 + 3y * 2) + 3(4x + 2y) = 0 (4x + 6y) + 3(4x + 2y) = 0 4x + 6y + (4x * 3 + 2y * 3) = 0 4x + 6y + (12x + 6y) = 0 Reorder the terms: 4x + 12x + 6y + 6y = 0 Combine like terms: 4x + 12x = 16x 16x + 6y + 6y = 0 Combine like terms: 6y + 6y = 12y 16x + 12y = 0 Solving 16x + 12y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12y' to each side of the equation. 16x + 12y + -12y = 0 + -12y Combine like terms: 12y + -12y = 0 16x + 0 = 0 + -12y 16x = 0 + -12y Remove the zero: 16x = -12y Divide each side by '16'. x = -0.75y Simplifying x = -0.75y
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