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Simplifying 3x(y + 2) + -6y(4 + x) + (x + 4)(3y + -2) = 0 Reorder the terms: 3x(2 + y) + -6y(4 + x) + (x + 4)(3y + -2) = 0 (2 * 3x + y * 3x) + -6y(4 + x) + (x + 4)(3y + -2) = 0 (6x + 3xy) + -6y(4 + x) + (x + 4)(3y + -2) = 0 6x + 3xy + (4 * -6y + x * -6y) + (x + 4)(3y + -2) = 0 Reorder the terms: 6x + 3xy + (-6xy + -24y) + (x + 4)(3y + -2) = 0 6x + 3xy + (-6xy + -24y) + (x + 4)(3y + -2) = 0 Reorder the terms: 6x + 3xy + -6xy + -24y + (4 + x)(3y + -2) = 0 Reorder the terms: 6x + 3xy + -6xy + -24y + (4 + x)(-2 + 3y) = 0 Multiply (4 + x) * (-2 + 3y) 6x + 3xy + -6xy + -24y + (4(-2 + 3y) + x(-2 + 3y)) = 0 6x + 3xy + -6xy + -24y + ((-2 * 4 + 3y * 4) + x(-2 + 3y)) = 0 6x + 3xy + -6xy + -24y + ((-8 + 12y) + x(-2 + 3y)) = 0 6x + 3xy + -6xy + -24y + (-8 + 12y + (-2 * x + 3y * x)) = 0 6x + 3xy + -6xy + -24y + (-8 + 12y + (-2x + 3xy)) = 0 Reorder the terms: 6x + 3xy + -6xy + -24y + (-8 + -2x + 3xy + 12y) = 0 6x + 3xy + -6xy + -24y + (-8 + -2x + 3xy + 12y) = 0 Reorder the terms: -8 + 6x + -2x + 3xy + -6xy + 3xy + -24y + 12y = 0 Combine like terms: 6x + -2x = 4x -8 + 4x + 3xy + -6xy + 3xy + -24y + 12y = 0 Combine like terms: 3xy + -6xy = -3xy -8 + 4x + -3xy + 3xy + -24y + 12y = 0 Combine like terms: -3xy + 3xy = 0 -8 + 4x + 0 + -24y + 12y = 0 -8 + 4x + -24y + 12y = 0 Combine like terms: -24y + 12y = -12y -8 + 4x + -12y = 0 Solving -8 + 4x + -12y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 4x + 8 + -12y = 0 + 8 Reorder the terms: -8 + 8 + 4x + -12y = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 4x + -12y = 0 + 8 4x + -12y = 0 + 8 Combine like terms: 0 + 8 = 8 4x + -12y = 8 Add '12y' to each side of the equation. 4x + -12y + 12y = 8 + 12y Combine like terms: -12y + 12y = 0 4x + 0 = 8 + 12y 4x = 8 + 12y Divide each side by '4'. x = 2 + 3y Simplifying x = 2 + 3y
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