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Simplifying (3x + 2)(4x + -1) = (6x + 1)(2x + -1) Reorder the terms: (2 + 3x)(4x + -1) = (6x + 1)(2x + -1) Reorder the terms: (2 + 3x)(-1 + 4x) = (6x + 1)(2x + -1) Multiply (2 + 3x) * (-1 + 4x) (2(-1 + 4x) + 3x * (-1 + 4x)) = (6x + 1)(2x + -1) ((-1 * 2 + 4x * 2) + 3x * (-1 + 4x)) = (6x + 1)(2x + -1) ((-2 + 8x) + 3x * (-1 + 4x)) = (6x + 1)(2x + -1) (-2 + 8x + (-1 * 3x + 4x * 3x)) = (6x + 1)(2x + -1) (-2 + 8x + (-3x + 12x2)) = (6x + 1)(2x + -1) Combine like terms: 8x + -3x = 5x (-2 + 5x + 12x2) = (6x + 1)(2x + -1) Reorder the terms: -2 + 5x + 12x2 = (1 + 6x)(2x + -1) Reorder the terms: -2 + 5x + 12x2 = (1 + 6x)(-1 + 2x) Multiply (1 + 6x) * (-1 + 2x) -2 + 5x + 12x2 = (1(-1 + 2x) + 6x * (-1 + 2x)) -2 + 5x + 12x2 = ((-1 * 1 + 2x * 1) + 6x * (-1 + 2x)) -2 + 5x + 12x2 = ((-1 + 2x) + 6x * (-1 + 2x)) -2 + 5x + 12x2 = (-1 + 2x + (-1 * 6x + 2x * 6x)) -2 + 5x + 12x2 = (-1 + 2x + (-6x + 12x2)) Combine like terms: 2x + -6x = -4x -2 + 5x + 12x2 = (-1 + -4x + 12x2) Add '-12x2' to each side of the equation. -2 + 5x + 12x2 + -12x2 = -1 + -4x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -2 + 5x + 0 = -1 + -4x + 12x2 + -12x2 -2 + 5x = -1 + -4x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -2 + 5x = -1 + -4x + 0 -2 + 5x = -1 + -4x Solving -2 + 5x = -1 + -4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4x' to each side of the equation. -2 + 5x + 4x = -1 + -4x + 4x Combine like terms: 5x + 4x = 9x -2 + 9x = -1 + -4x + 4x Combine like terms: -4x + 4x = 0 -2 + 9x = -1 + 0 -2 + 9x = -1 Add '2' to each side of the equation. -2 + 2 + 9x = -1 + 2 Combine like terms: -2 + 2 = 0 0 + 9x = -1 + 2 9x = -1 + 2 Combine like terms: -1 + 2 = 1 9x = 1 Divide each side by '9'. x = 0.1111111111 Simplifying x = 0.1111111111
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