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