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Simplifying 4(2x + -3y) + -2(6x + -4y) + 3y = 0 (2x * 4 + -3y * 4) + -2(6x + -4y) + 3y = 0 (8x + -12y) + -2(6x + -4y) + 3y = 0 8x + -12y + (6x * -2 + -4y * -2) + 3y = 0 8x + -12y + (-12x + 8y) + 3y = 0 Reorder the terms: 8x + -12x + -12y + 8y + 3y = 0 Combine like terms: 8x + -12x = -4x -4x + -12y + 8y + 3y = 0 Combine like terms: -12y + 8y = -4y -4x + -4y + 3y = 0 Combine like terms: -4y + 3y = -1y -4x + -1y = 0 Solving -4x + -1y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. -4x + -1y + y = 0 + y Combine like terms: -1y + y = 0 -4x + 0 = 0 + y -4x = 0 + y Remove the zero: -4x = y Divide each side by '-4'. x = -0.25y Simplifying x = -0.25y
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