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Simplifying (x + 5)(x + -2 + 3i) = 0 Reorder the terms: (5 + x)(x + -2 + 3i) = 0 Reorder the terms: (5 + x)(-2 + 3i + x) = 0 Multiply (5 + x) * (-2 + 3i + x) (5(-2 + 3i + x) + x(-2 + 3i + x)) = 0 ((-2 * 5 + 3i * 5 + x * 5) + x(-2 + 3i + x)) = 0 ((-10 + 15i + 5x) + x(-2 + 3i + x)) = 0 (-10 + 15i + 5x + (-2 * x + 3i * x + x * x)) = 0 Reorder the terms: (-10 + 15i + 5x + (3ix + -2x + x2)) = 0 (-10 + 15i + 5x + (3ix + -2x + x2)) = 0 Reorder the terms: (-10 + 15i + 3ix + 5x + -2x + x2) = 0 Combine like terms: 5x + -2x = 3x (-10 + 15i + 3ix + 3x + x2) = 0 Solving -10 + 15i + 3ix + 3x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 15i + 3ix + 3x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 15i + 3ix + 3x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 15i + 3ix + 3x + x2 = 0 + 10 15i + 3ix + 3x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 15i + 3ix + 3x + x2 = 10 Add '-3x' to each side of the equation. 15i + 3ix + 3x + -3x + x2 = 10 + -3x Combine like terms: 3x + -3x = 0 15i + 3ix + 0 + x2 = 10 + -3x 15i + 3ix + x2 = 10 + -3x Add '-1x2' to each side of the equation. 15i + 3ix + x2 + -1x2 = 10 + -3x + -1x2 Combine like terms: x2 + -1x2 = 0 15i + 3ix + 0 = 10 + -3x + -1x2 15i + 3ix = 10 + -3x + -1x2 Reorder the terms: -10 + 15i + 3ix + 3x + x2 = 10 + -3x + -1x2 + -10 + 3x + x2 Reorder the terms: -10 + 15i + 3ix + 3x + x2 = 10 + -10 + -3x + 3x + -1x2 + x2 Combine like terms: 10 + -10 = 0 -10 + 15i + 3ix + 3x + x2 = 0 + -3x + 3x + -1x2 + x2 -10 + 15i + 3ix + 3x + x2 = -3x + 3x + -1x2 + x2 Combine like terms: -3x + 3x = 0 -10 + 15i + 3ix + 3x + x2 = 0 + -1x2 + x2 -10 + 15i + 3ix + 3x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -10 + 15i + 3ix + 3x + x2 = 0 The solution to this equation could not be determined.
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