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Simplifying (3x + 2)(2x + -1) + 5x = 4 + (3x + 1)(2x + 1) Reorder the terms: (2 + 3x)(2x + -1) + 5x = 4 + (3x + 1)(2x + 1) Reorder the terms: (2 + 3x)(-1 + 2x) + 5x = 4 + (3x + 1)(2x + 1) Multiply (2 + 3x) * (-1 + 2x) (2(-1 + 2x) + 3x * (-1 + 2x)) + 5x = 4 + (3x + 1)(2x + 1) ((-1 * 2 + 2x * 2) + 3x * (-1 + 2x)) + 5x = 4 + (3x + 1)(2x + 1) ((-2 + 4x) + 3x * (-1 + 2x)) + 5x = 4 + (3x + 1)(2x + 1) (-2 + 4x + (-1 * 3x + 2x * 3x)) + 5x = 4 + (3x + 1)(2x + 1) (-2 + 4x + (-3x + 6x2)) + 5x = 4 + (3x + 1)(2x + 1) Combine like terms: 4x + -3x = 1x (-2 + 1x + 6x2) + 5x = 4 + (3x + 1)(2x + 1) Reorder the terms: -2 + 1x + 5x + 6x2 = 4 + (3x + 1)(2x + 1) Combine like terms: 1x + 5x = 6x -2 + 6x + 6x2 = 4 + (3x + 1)(2x + 1) Reorder the terms: -2 + 6x + 6x2 = 4 + (1 + 3x)(2x + 1) Reorder the terms: -2 + 6x + 6x2 = 4 + (1 + 3x)(1 + 2x) Multiply (1 + 3x) * (1 + 2x) -2 + 6x + 6x2 = 4 + (1(1 + 2x) + 3x * (1 + 2x)) -2 + 6x + 6x2 = 4 + ((1 * 1 + 2x * 1) + 3x * (1 + 2x)) -2 + 6x + 6x2 = 4 + ((1 + 2x) + 3x * (1 + 2x)) -2 + 6x + 6x2 = 4 + (1 + 2x + (1 * 3x + 2x * 3x)) -2 + 6x + 6x2 = 4 + (1 + 2x + (3x + 6x2)) Combine like terms: 2x + 3x = 5x -2 + 6x + 6x2 = 4 + (1 + 5x + 6x2) Combine like terms: 4 + 1 = 5 -2 + 6x + 6x2 = 5 + 5x + 6x2 Add '-6x2' to each side of the equation. -2 + 6x + 6x2 + -6x2 = 5 + 5x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -2 + 6x + 0 = 5 + 5x + 6x2 + -6x2 -2 + 6x = 5 + 5x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -2 + 6x = 5 + 5x + 0 -2 + 6x = 5 + 5x Solving -2 + 6x = 5 + 5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5x' to each side of the equation. -2 + 6x + -5x = 5 + 5x + -5x Combine like terms: 6x + -5x = 1x -2 + 1x = 5 + 5x + -5x Combine like terms: 5x + -5x = 0 -2 + 1x = 5 + 0 -2 + 1x = 5 Add '2' to each side of the equation. -2 + 2 + 1x = 5 + 2 Combine like terms: -2 + 2 = 0 0 + 1x = 5 + 2 1x = 5 + 2 Combine like terms: 5 + 2 = 7 1x = 7 Divide each side by '1'. x = 7 Simplifying x = 7
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