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