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Simplifying (x + -1)(4x + 2) = (2x + 3)(2 + 2x) Reorder the terms: (-1 + x)(4x + 2) = (2x + 3)(2 + 2x) Reorder the terms: (-1 + x)(2 + 4x) = (2x + 3)(2 + 2x) Multiply (-1 + x) * (2 + 4x) (-1(2 + 4x) + x(2 + 4x)) = (2x + 3)(2 + 2x) ((2 * -1 + 4x * -1) + x(2 + 4x)) = (2x + 3)(2 + 2x) ((-2 + -4x) + x(2 + 4x)) = (2x + 3)(2 + 2x) (-2 + -4x + (2 * x + 4x * x)) = (2x + 3)(2 + 2x) (-2 + -4x + (2x + 4x2)) = (2x + 3)(2 + 2x) Combine like terms: -4x + 2x = -2x (-2 + -2x + 4x2) = (2x + 3)(2 + 2x) Reorder the terms: -2 + -2x + 4x2 = (3 + 2x)(2 + 2x) Multiply (3 + 2x) * (2 + 2x) -2 + -2x + 4x2 = (3(2 + 2x) + 2x * (2 + 2x)) -2 + -2x + 4x2 = ((2 * 3 + 2x * 3) + 2x * (2 + 2x)) -2 + -2x + 4x2 = ((6 + 6x) + 2x * (2 + 2x)) -2 + -2x + 4x2 = (6 + 6x + (2 * 2x + 2x * 2x)) -2 + -2x + 4x2 = (6 + 6x + (4x + 4x2)) Combine like terms: 6x + 4x = 10x -2 + -2x + 4x2 = (6 + 10x + 4x2) Add '-4x2' to each side of the equation. -2 + -2x + 4x2 + -4x2 = 6 + 10x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -2 + -2x + 0 = 6 + 10x + 4x2 + -4x2 -2 + -2x = 6 + 10x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -2 + -2x = 6 + 10x + 0 -2 + -2x = 6 + 10x Solving -2 + -2x = 6 + 10x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10x' to each side of the equation. -2 + -2x + -10x = 6 + 10x + -10x Combine like terms: -2x + -10x = -12x -2 + -12x = 6 + 10x + -10x Combine like terms: 10x + -10x = 0 -2 + -12x = 6 + 0 -2 + -12x = 6 Add '2' to each side of the equation. -2 + 2 + -12x = 6 + 2 Combine like terms: -2 + 2 = 0 0 + -12x = 6 + 2 -12x = 6 + 2 Combine like terms: 6 + 2 = 8 -12x = 8 Divide each side by '-12'. x = -0.6666666667 Simplifying x = -0.6666666667
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