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Simplifying (x + 7i)(x + -7i)(x + 3) = 0 Reorder the terms: (7i + x)(x + -7i)(x + 3) = 0 Reorder the terms: (7i + x)(-7i + x)(x + 3) = 0 Reorder the terms: (7i + x)(-7i + x)(3 + x) = 0 Multiply (7i + x) * (-7i + x) (7i * (-7i + x) + x(-7i + x))(3 + x) = 0 ((-7i * 7i + x * 7i) + x(-7i + x))(3 + x) = 0 Reorder the terms: ((7ix + -49i2) + x(-7i + x))(3 + x) = 0 ((7ix + -49i2) + x(-7i + x))(3 + x) = 0 (7ix + -49i2 + (-7i * x + x * x))(3 + x) = 0 (7ix + -49i2 + (-7ix + x2))(3 + x) = 0 Reorder the terms: (7ix + -7ix + -49i2 + x2)(3 + x) = 0 Combine like terms: 7ix + -7ix = 0 (0 + -49i2 + x2)(3 + x) = 0 (-49i2 + x2)(3 + x) = 0 Multiply (-49i2 + x2) * (3 + x) (-49i2 * (3 + x) + x2(3 + x)) = 0 ((3 * -49i2 + x * -49i2) + x2(3 + x)) = 0 ((-147i2 + -49i2x) + x2(3 + x)) = 0 (-147i2 + -49i2x + (3 * x2 + x * x2)) = 0 (-147i2 + -49i2x + (3x2 + x3)) = 0 (-147i2 + -49i2x + 3x2 + x3) = 0 Solving -147i2 + -49i2x + 3x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3x2' to each side of the equation. -147i2 + -49i2x + 3x2 + -3x2 + x3 = 0 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -147i2 + -49i2x + 0 + x3 = 0 + -3x2 -147i2 + -49i2x + x3 = 0 + -3x2 Remove the zero: -147i2 + -49i2x + x3 = -3x2 Add '-1x3' to each side of the equation. -147i2 + -49i2x + x3 + -1x3 = -3x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -147i2 + -49i2x + 0 = -3x2 + -1x3 -147i2 + -49i2x = -3x2 + -1x3 Reorder the terms: -147i2 + -49i2x + 3x2 + x3 = -3x2 + 3x2 + -1x3 + x3 Combine like terms: -3x2 + 3x2 = 0 -147i2 + -49i2x + 3x2 + x3 = 0 + -1x3 + x3 -147i2 + -49i2x + 3x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -147i2 + -49i2x + 3x2 + x3 = 0 The solution to this equation could not be determined.
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