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Simplifying (4x + -1)(x + 5) = (2x + 1)(2x + 7) Reorder the terms: (-1 + 4x)(x + 5) = (2x + 1)(2x + 7) Reorder the terms: (-1 + 4x)(5 + x) = (2x + 1)(2x + 7) Multiply (-1 + 4x) * (5 + x) (-1(5 + x) + 4x * (5 + x)) = (2x + 1)(2x + 7) ((5 * -1 + x * -1) + 4x * (5 + x)) = (2x + 1)(2x + 7) ((-5 + -1x) + 4x * (5 + x)) = (2x + 1)(2x + 7) (-5 + -1x + (5 * 4x + x * 4x)) = (2x + 1)(2x + 7) (-5 + -1x + (20x + 4x2)) = (2x + 1)(2x + 7) Combine like terms: -1x + 20x = 19x (-5 + 19x + 4x2) = (2x + 1)(2x + 7) Reorder the terms: -5 + 19x + 4x2 = (1 + 2x)(2x + 7) Reorder the terms: -5 + 19x + 4x2 = (1 + 2x)(7 + 2x) Multiply (1 + 2x) * (7 + 2x) -5 + 19x + 4x2 = (1(7 + 2x) + 2x * (7 + 2x)) -5 + 19x + 4x2 = ((7 * 1 + 2x * 1) + 2x * (7 + 2x)) -5 + 19x + 4x2 = ((7 + 2x) + 2x * (7 + 2x)) -5 + 19x + 4x2 = (7 + 2x + (7 * 2x + 2x * 2x)) -5 + 19x + 4x2 = (7 + 2x + (14x + 4x2)) Combine like terms: 2x + 14x = 16x -5 + 19x + 4x2 = (7 + 16x + 4x2) Add '-4x2' to each side of the equation. -5 + 19x + 4x2 + -4x2 = 7 + 16x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -5 + 19x + 0 = 7 + 16x + 4x2 + -4x2 -5 + 19x = 7 + 16x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -5 + 19x = 7 + 16x + 0 -5 + 19x = 7 + 16x Solving -5 + 19x = 7 + 16x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16x' to each side of the equation. -5 + 19x + -16x = 7 + 16x + -16x Combine like terms: 19x + -16x = 3x -5 + 3x = 7 + 16x + -16x Combine like terms: 16x + -16x = 0 -5 + 3x = 7 + 0 -5 + 3x = 7 Add '5' to each side of the equation. -5 + 5 + 3x = 7 + 5 Combine like terms: -5 + 5 = 0 0 + 3x = 7 + 5 3x = 7 + 5 Combine like terms: 7 + 5 = 12 3x = 12 Divide each side by '3'. x = 4 Simplifying x = 4
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