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Simplifying (4x + -1)(2x + -1) = (4x + 1)(2x + 1) Reorder the terms: (-1 + 4x)(2x + -1) = (4x + 1)(2x + 1) Reorder the terms: (-1 + 4x)(-1 + 2x) = (4x + 1)(2x + 1) Multiply (-1 + 4x) * (-1 + 2x) (-1(-1 + 2x) + 4x * (-1 + 2x)) = (4x + 1)(2x + 1) ((-1 * -1 + 2x * -1) + 4x * (-1 + 2x)) = (4x + 1)(2x + 1) ((1 + -2x) + 4x * (-1 + 2x)) = (4x + 1)(2x + 1) (1 + -2x + (-1 * 4x + 2x * 4x)) = (4x + 1)(2x + 1) (1 + -2x + (-4x + 8x2)) = (4x + 1)(2x + 1) Combine like terms: -2x + -4x = -6x (1 + -6x + 8x2) = (4x + 1)(2x + 1) Reorder the terms: 1 + -6x + 8x2 = (1 + 4x)(2x + 1) Reorder the terms: 1 + -6x + 8x2 = (1 + 4x)(1 + 2x) Multiply (1 + 4x) * (1 + 2x) 1 + -6x + 8x2 = (1(1 + 2x) + 4x * (1 + 2x)) 1 + -6x + 8x2 = ((1 * 1 + 2x * 1) + 4x * (1 + 2x)) 1 + -6x + 8x2 = ((1 + 2x) + 4x * (1 + 2x)) 1 + -6x + 8x2 = (1 + 2x + (1 * 4x + 2x * 4x)) 1 + -6x + 8x2 = (1 + 2x + (4x + 8x2)) Combine like terms: 2x + 4x = 6x 1 + -6x + 8x2 = (1 + 6x + 8x2) Add '-1' to each side of the equation. 1 + -6x + -1 + 8x2 = 1 + 6x + -1 + 8x2 Reorder the terms: 1 + -1 + -6x + 8x2 = 1 + 6x + -1 + 8x2 Combine like terms: 1 + -1 = 0 0 + -6x + 8x2 = 1 + 6x + -1 + 8x2 -6x + 8x2 = 1 + 6x + -1 + 8x2 Reorder the terms: -6x + 8x2 = 1 + -1 + 6x + 8x2 Combine like terms: 1 + -1 = 0 -6x + 8x2 = 0 + 6x + 8x2 -6x + 8x2 = 6x + 8x2 Add '-8x2' to each side of the equation. -6x + 8x2 + -8x2 = 6x + 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -6x + 0 = 6x + 8x2 + -8x2 -6x = 6x + 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -6x = 6x + 0 -6x = 6x Solving -6x = 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. -6x + -6x = 6x + -6x Combine like terms: -6x + -6x = -12x -12x = 6x + -6x Combine like terms: 6x + -6x = 0 -12x = 0 Divide each side by '-12'. x = 0 Simplifying x = 0
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