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Simplifying (x + 3)(x + k)(x + -5) = -3 Reorder the terms: (3 + x)(x + k)(x + -5) = -3 Reorder the terms: (3 + x)(k + x)(x + -5) = -3 Reorder the terms: (3 + x)(k + x)(-5 + x) = -3 Multiply (3 + x) * (k + x) (3(k + x) + x(k + x))(-5 + x) = -3 ((k * 3 + x * 3) + x(k + x))(-5 + x) = -3 ((3k + 3x) + x(k + x))(-5 + x) = -3 (3k + 3x + (k * x + x * x))(-5 + x) = -3 (3k + 3x + (kx + x2))(-5 + x) = -3 Reorder the terms: (3k + kx + 3x + x2)(-5 + x) = -3 (3k + kx + 3x + x2)(-5 + x) = -3 Multiply (3k + kx + 3x + x2) * (-5 + x) (3k * (-5 + x) + kx(-5 + x) + 3x * (-5 + x) + x2(-5 + x)) = -3 ((-5 * 3k + x * 3k) + kx(-5 + x) + 3x * (-5 + x) + x2(-5 + x)) = -3 ((-15k + 3kx) + kx(-5 + x) + 3x * (-5 + x) + x2(-5 + x)) = -3 (-15k + 3kx + (-5 * kx + x * kx) + 3x * (-5 + x) + x2(-5 + x)) = -3 (-15k + 3kx + (-5kx + kx2) + 3x * (-5 + x) + x2(-5 + x)) = -3 (-15k + 3kx + -5kx + kx2 + (-5 * 3x + x * 3x) + x2(-5 + x)) = -3 (-15k + 3kx + -5kx + kx2 + (-15x + 3x2) + x2(-5 + x)) = -3 (-15k + 3kx + -5kx + kx2 + -15x + 3x2 + (-5 * x2 + x * x2)) = -3 (-15k + 3kx + -5kx + kx2 + -15x + 3x2 + (-5x2 + x3)) = -3 Combine like terms: 3kx + -5kx = -2kx (-15k + -2kx + kx2 + -15x + 3x2 + -5x2 + x3) = -3 Combine like terms: 3x2 + -5x2 = -2x2 (-15k + -2kx + kx2 + -15x + -2x2 + x3) = -3 Solving -15k + -2kx + kx2 + -15x + -2x2 + x3 = -3 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '15x' to each side of the equation. -15k + -2kx + kx2 + -15x + -2x2 + 15x + x3 = -3 + 15x Reorder the terms: -15k + -2kx + kx2 + -15x + 15x + -2x2 + x3 = -3 + 15x Combine like terms: -15x + 15x = 0 -15k + -2kx + kx2 + 0 + -2x2 + x3 = -3 + 15x -15k + -2kx + kx2 + -2x2 + x3 = -3 + 15x Add '2x2' to each side of the equation. -15k + -2kx + kx2 + -2x2 + 2x2 + x3 = -3 + 15x + 2x2 Combine like terms: -2x2 + 2x2 = 0 -15k + -2kx + kx2 + 0 + x3 = -3 + 15x + 2x2 -15k + -2kx + kx2 + x3 = -3 + 15x + 2x2 Add '-1x3' to each side of the equation. -15k + -2kx + kx2 + x3 + -1x3 = -3 + 15x + 2x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -15k + -2kx + kx2 + 0 = -3 + 15x + 2x2 + -1x3 -15k + -2kx + kx2 = -3 + 15x + 2x2 + -1x3 Reorder the terms: 3 + -15k + -2kx + kx2 + -15x + -2x2 + x3 = -3 + 15x + 2x2 + -1x3 + 3 + -15x + -2x2 + x3 Reorder the terms: 3 + -15k + -2kx + kx2 + -15x + -2x2 + x3 = -3 + 3 + 15x + -15x + 2x2 + -2x2 + -1x3 + x3 Combine like terms: -3 + 3 = 0 3 + -15k + -2kx + kx2 + -15x + -2x2 + x3 = 0 + 15x + -15x + 2x2 + -2x2 + -1x3 + x3 3 + -15k + -2kx + kx2 + -15x + -2x2 + x3 = 15x + -15x + 2x2 + -2x2 + -1x3 + x3 Combine like terms: 15x + -15x = 0 3 + -15k + -2kx + kx2 + -15x + -2x2 + x3 = 0 + 2x2 + -2x2 + -1x3 + x3 3 + -15k + -2kx + kx2 + -15x + -2x2 + x3 = 2x2 + -2x2 + -1x3 + x3 Combine like terms: 2x2 + -2x2 = 0 3 + -15k + -2kx + kx2 + -15x + -2x2 + x3 = 0 + -1x3 + x3 3 + -15k + -2kx + kx2 + -15x + -2x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 3 + -15k + -2kx + kx2 + -15x + -2x2 + x3 = 0 The solution to this equation could not be determined.
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