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Simplifying (3x + 1)(2x + 1) = 2x(3x + 1) Reorder the terms: (1 + 3x)(2x + 1) = 2x(3x + 1) Reorder the terms: (1 + 3x)(1 + 2x) = 2x(3x + 1) Multiply (1 + 3x) * (1 + 2x) (1(1 + 2x) + 3x * (1 + 2x)) = 2x(3x + 1) ((1 * 1 + 2x * 1) + 3x * (1 + 2x)) = 2x(3x + 1) ((1 + 2x) + 3x * (1 + 2x)) = 2x(3x + 1) (1 + 2x + (1 * 3x + 2x * 3x)) = 2x(3x + 1) (1 + 2x + (3x + 6x2)) = 2x(3x + 1) Combine like terms: 2x + 3x = 5x (1 + 5x + 6x2) = 2x(3x + 1) Reorder the terms: 1 + 5x + 6x2 = 2x(1 + 3x) 1 + 5x + 6x2 = (1 * 2x + 3x * 2x) 1 + 5x + 6x2 = (2x + 6x2) Add '-6x2' to each side of the equation. 1 + 5x + 6x2 + -6x2 = 2x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 1 + 5x + 0 = 2x + 6x2 + -6x2 1 + 5x = 2x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 1 + 5x = 2x + 0 1 + 5x = 2x Solving 1 + 5x = 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. 1 + 5x + -2x = 2x + -2x Combine like terms: 5x + -2x = 3x 1 + 3x = 2x + -2x Combine like terms: 2x + -2x = 0 1 + 3x = 0 Add '-1' to each side of the equation. 1 + -1 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333
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