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Simplifying x(x + -1) + 4(x + 1) = x(x + 1) Reorder the terms: x(-1 + x) + 4(x + 1) = x(x + 1) (-1 * x + x * x) + 4(x + 1) = x(x + 1) (-1x + x2) + 4(x + 1) = x(x + 1) Reorder the terms: -1x + x2 + 4(1 + x) = x(x + 1) -1x + x2 + (1 * 4 + x * 4) = x(x + 1) -1x + x2 + (4 + 4x) = x(x + 1) Reorder the terms: 4 + -1x + 4x + x2 = x(x + 1) Combine like terms: -1x + 4x = 3x 4 + 3x + x2 = x(x + 1) Reorder the terms: 4 + 3x + x2 = x(1 + x) 4 + 3x + x2 = (1 * x + x * x) 4 + 3x + x2 = (1x + x2) Add '-1x2' to each side of the equation. 4 + 3x + x2 + -1x2 = 1x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4 + 3x + 0 = 1x + x2 + -1x2 4 + 3x = 1x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4 + 3x = 1x + 0 4 + 3x = 1x Solving 4 + 3x = 1x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1x' to each side of the equation. 4 + 3x + -1x = 1x + -1x Combine like terms: 3x + -1x = 2x 4 + 2x = 1x + -1x Combine like terms: 1x + -1x = 0 4 + 2x = 0 Add '-4' to each side of the equation. 4 + -4 + 2x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2x = 0 + -4 2x = 0 + -4 Combine like terms: 0 + -4 = -4 2x = -4 Divide each side by '2'. x = -2 Simplifying x = -2
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