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Simplifying (2x + -1)(x2 + 4r + -4) = 0 Reorder the terms: (-1 + 2x)(x2 + 4r + -4) = 0 Reorder the terms: (-1 + 2x)(-4 + 4r + x2) = 0 Multiply (-1 + 2x) * (-4 + 4r + x2) (-1(-4 + 4r + x2) + 2x * (-4 + 4r + x2)) = 0 ((-4 * -1 + 4r * -1 + x2 * -1) + 2x * (-4 + 4r + x2)) = 0 ((4 + -4r + -1x2) + 2x * (-4 + 4r + x2)) = 0 (4 + -4r + -1x2 + (-4 * 2x + 4r * 2x + x2 * 2x)) = 0 Reorder the terms: (4 + -4r + -1x2 + (8rx + -8x + 2x3)) = 0 (4 + -4r + -1x2 + (8rx + -8x + 2x3)) = 0 Reorder the terms: (4 + -4r + 8rx + -8x + -1x2 + 2x3) = 0 (4 + -4r + 8rx + -8x + -1x2 + 2x3) = 0 Solving 4 + -4r + 8rx + -8x + -1x2 + 2x3 = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4r + 8rx + -8x + -1x2 + -4 + 2x3 = 0 + -4 Reorder the terms: 4 + -4 + -4r + 8rx + -8x + -1x2 + 2x3 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4r + 8rx + -8x + -1x2 + 2x3 = 0 + -4 -4r + 8rx + -8x + -1x2 + 2x3 = 0 + -4 Combine like terms: 0 + -4 = -4 -4r + 8rx + -8x + -1x2 + 2x3 = -4 Add '8x' to each side of the equation. -4r + 8rx + -8x + -1x2 + 8x + 2x3 = -4 + 8x Reorder the terms: -4r + 8rx + -8x + 8x + -1x2 + 2x3 = -4 + 8x Combine like terms: -8x + 8x = 0 -4r + 8rx + 0 + -1x2 + 2x3 = -4 + 8x -4r + 8rx + -1x2 + 2x3 = -4 + 8x Add 'x2' to each side of the equation. -4r + 8rx + -1x2 + x2 + 2x3 = -4 + 8x + x2 Combine like terms: -1x2 + x2 = 0 -4r + 8rx + 0 + 2x3 = -4 + 8x + x2 -4r + 8rx + 2x3 = -4 + 8x + x2 Add '-2x3' to each side of the equation. -4r + 8rx + 2x3 + -2x3 = -4 + 8x + x2 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -4r + 8rx + 0 = -4 + 8x + x2 + -2x3 -4r + 8rx = -4 + 8x + x2 + -2x3 Reorder the terms: 4 + -4r + 8rx + -8x + -1x2 + 2x3 = -4 + 8x + x2 + -2x3 + 4 + -8x + -1x2 + 2x3 Reorder the terms: 4 + -4r + 8rx + -8x + -1x2 + 2x3 = -4 + 4 + 8x + -8x + x2 + -1x2 + -2x3 + 2x3 Combine like terms: -4 + 4 = 0 4 + -4r + 8rx + -8x + -1x2 + 2x3 = 0 + 8x + -8x + x2 + -1x2 + -2x3 + 2x3 4 + -4r + 8rx + -8x + -1x2 + 2x3 = 8x + -8x + x2 + -1x2 + -2x3 + 2x3 Combine like terms: 8x + -8x = 0 4 + -4r + 8rx + -8x + -1x2 + 2x3 = 0 + x2 + -1x2 + -2x3 + 2x3 4 + -4r + 8rx + -8x + -1x2 + 2x3 = x2 + -1x2 + -2x3 + 2x3 Combine like terms: x2 + -1x2 = 0 4 + -4r + 8rx + -8x + -1x2 + 2x3 = 0 + -2x3 + 2x3 4 + -4r + 8rx + -8x + -1x2 + 2x3 = -2x3 + 2x3 Combine like terms: -2x3 + 2x3 = 0 4 + -4r + 8rx + -8x + -1x2 + 2x3 = 0 The solution to this equation could not be determined.
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