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Simplifying x(x + 1) + (x + 3)(x + 1) = 2x(x + 3) Reorder the terms: x(1 + x) + (x + 3)(x + 1) = 2x(x + 3) (1 * x + x * x) + (x + 3)(x + 1) = 2x(x + 3) (1x + x2) + (x + 3)(x + 1) = 2x(x + 3) Reorder the terms: 1x + x2 + (3 + x)(x + 1) = 2x(x + 3) Reorder the terms: 1x + x2 + (3 + x)(1 + x) = 2x(x + 3) Multiply (3 + x) * (1 + x) 1x + x2 + (3(1 + x) + x(1 + x)) = 2x(x + 3) 1x + x2 + ((1 * 3 + x * 3) + x(1 + x)) = 2x(x + 3) 1x + x2 + ((3 + 3x) + x(1 + x)) = 2x(x + 3) 1x + x2 + (3 + 3x + (1 * x + x * x)) = 2x(x + 3) 1x + x2 + (3 + 3x + (1x + x2)) = 2x(x + 3) Combine like terms: 3x + 1x = 4x 1x + x2 + (3 + 4x + x2) = 2x(x + 3) Reorder the terms: 3 + 1x + 4x + x2 + x2 = 2x(x + 3) Combine like terms: 1x + 4x = 5x 3 + 5x + x2 + x2 = 2x(x + 3) Combine like terms: x2 + x2 = 2x2 3 + 5x + 2x2 = 2x(x + 3) Reorder the terms: 3 + 5x + 2x2 = 2x(3 + x) 3 + 5x + 2x2 = (3 * 2x + x * 2x) 3 + 5x + 2x2 = (6x + 2x2) Add '-2x2' to each side of the equation. 3 + 5x + 2x2 + -2x2 = 6x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 3 + 5x + 0 = 6x + 2x2 + -2x2 3 + 5x = 6x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 3 + 5x = 6x + 0 3 + 5x = 6x Solving 3 + 5x = 6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6x' to each side of the equation. 3 + 5x + -6x = 6x + -6x Combine like terms: 5x + -6x = -1x 3 + -1x = 6x + -6x Combine like terms: 6x + -6x = 0 3 + -1x = 0 Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3
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