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Simplifying (x + -5)(xb + 2x + 1) = x(x + 1)(x + -4) Reorder the terms: (-5 + x)(xb + 2x + 1) = x(x + 1)(x + -4) Reorder the terms: (-5 + x)(1 + bx + 2x) = x(x + 1)(x + -4) Multiply (-5 + x) * (1 + bx + 2x) (-5(1 + bx + 2x) + x(1 + bx + 2x)) = x(x + 1)(x + -4) ((1 * -5 + bx * -5 + 2x * -5) + x(1 + bx + 2x)) = x(x + 1)(x + -4) ((-5 + -5bx + -10x) + x(1 + bx + 2x)) = x(x + 1)(x + -4) (-5 + -5bx + -10x + (1 * x + bx * x + 2x * x)) = x(x + 1)(x + -4) Reorder the terms: (-5 + -5bx + -10x + (bx2 + 1x + 2x2)) = x(x + 1)(x + -4) (-5 + -5bx + -10x + (bx2 + 1x + 2x2)) = x(x + 1)(x + -4) Reorder the terms: (-5 + -5bx + bx2 + -10x + 1x + 2x2) = x(x + 1)(x + -4) Combine like terms: -10x + 1x = -9x (-5 + -5bx + bx2 + -9x + 2x2) = x(x + 1)(x + -4) Reorder the terms: -5 + -5bx + bx2 + -9x + 2x2 = x(1 + x)(x + -4) Reorder the terms: -5 + -5bx + bx2 + -9x + 2x2 = x(1 + x)(-4 + x) Multiply (1 + x) * (-4 + x) -5 + -5bx + bx2 + -9x + 2x2 = x(1(-4 + x) + x(-4 + x)) -5 + -5bx + bx2 + -9x + 2x2 = x((-4 * 1 + x * 1) + x(-4 + x)) -5 + -5bx + bx2 + -9x + 2x2 = x((-4 + 1x) + x(-4 + x)) -5 + -5bx + bx2 + -9x + 2x2 = x(-4 + 1x + (-4 * x + x * x)) -5 + -5bx + bx2 + -9x + 2x2 = x(-4 + 1x + (-4x + x2)) Combine like terms: 1x + -4x = -3x -5 + -5bx + bx2 + -9x + 2x2 = x(-4 + -3x + x2) -5 + -5bx + bx2 + -9x + 2x2 = (-4 * x + -3x * x + x2 * x) -5 + -5bx + bx2 + -9x + 2x2 = (-4x + -3x2 + x3) Solving -5 + -5bx + bx2 + -9x + 2x2 = -4x + -3x2 + x3 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + -5bx + bx2 + -9x + 5 + 2x2 = -4x + -3x2 + 5 + x3 Reorder the terms: -5 + 5 + -5bx + bx2 + -9x + 2x2 = -4x + -3x2 + 5 + x3 Combine like terms: -5 + 5 = 0 0 + -5bx + bx2 + -9x + 2x2 = -4x + -3x2 + 5 + x3 -5bx + bx2 + -9x + 2x2 = -4x + -3x2 + 5 + x3 Reorder the terms: -5bx + bx2 + -9x + 2x2 = 5 + -4x + -3x2 + x3 Add '9x' to each side of the equation. -5bx + bx2 + -9x + 9x + 2x2 = 5 + -4x + -3x2 + 9x + x3 Combine like terms: -9x + 9x = 0 -5bx + bx2 + 0 + 2x2 = 5 + -4x + -3x2 + 9x + x3 -5bx + bx2 + 2x2 = 5 + -4x + -3x2 + 9x + x3 Reorder the terms: -5bx + bx2 + 2x2 = 5 + -4x + 9x + -3x2 + x3 Combine like terms: -4x + 9x = 5x -5bx + bx2 + 2x2 = 5 + 5x + -3x2 + x3 Add '-2x2' to each side of the equation. -5bx + bx2 + 2x2 + -2x2 = 5 + 5x + -3x2 + -2x2 + x3 Combine like terms: 2x2 + -2x2 = 0 -5bx + bx2 + 0 = 5 + 5x + -3x2 + -2x2 + x3 -5bx + bx2 = 5 + 5x + -3x2 + -2x2 + x3 Combine like terms: -3x2 + -2x2 = -5x2 -5bx + bx2 = 5 + 5x + -5x2 + x3 Reorder the terms: -5 + -5bx + bx2 + -5x + 5x2 + -1x3 = 5 + 5x + -5x2 + x3 + -5 + -5x + 5x2 + -1x3 Reorder the terms: -5 + -5bx + bx2 + -5x + 5x2 + -1x3 = 5 + -5 + 5x + -5x + -5x2 + 5x2 + x3 + -1x3 Combine like terms: 5 + -5 = 0 -5 + -5bx + bx2 + -5x + 5x2 + -1x3 = 0 + 5x + -5x + -5x2 + 5x2 + x3 + -1x3 -5 + -5bx + bx2 + -5x + 5x2 + -1x3 = 5x + -5x + -5x2 + 5x2 + x3 + -1x3 Combine like terms: 5x + -5x = 0 -5 + -5bx + bx2 + -5x + 5x2 + -1x3 = 0 + -5x2 + 5x2 + x3 + -1x3 -5 + -5bx + bx2 + -5x + 5x2 + -1x3 = -5x2 + 5x2 + x3 + -1x3 Combine like terms: -5x2 + 5x2 = 0 -5 + -5bx + bx2 + -5x + 5x2 + -1x3 = 0 + x3 + -1x3 -5 + -5bx + bx2 + -5x + 5x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -5 + -5bx + bx2 + -5x + 5x2 + -1x3 = 0 The solution to this equation could not be determined.
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