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Simplifying (x + 2)(x + 0)(x + -3i)(x + 3i) = 0 Reorder the terms: (2 + x)(x + 0)(x + -3i)(x + 3i) = 0 Reorder the terms: (2 + x)(0 + x)(x + -3i)(x + 3i) = 0 Remove the zero: (2 + x)(x)(x + -3i)(x + 3i) = 0 Reorder the terms: (2 + x) * x(-3i + x)(x + 3i) = 0 Reorder the terms: (2 + x) * x(-3i + x)(3i + x) = 0 Reorder the terms for easier multiplication: x(2 + x)(-3i + x)(3i + x) = 0 Multiply (2 + x) * (-3i + x) x(2(-3i + x) + x(-3i + x))(3i + x) = 0 x((-3i * 2 + x * 2) + x(-3i + x))(3i + x) = 0 x((-6i + 2x) + x(-3i + x))(3i + x) = 0 x(-6i + 2x + (-3i * x + x * x))(3i + x) = 0 x(-6i + 2x + (-3ix + x2))(3i + x) = 0 Reorder the terms: x(-6i + -3ix + 2x + x2)(3i + x) = 0 x(-6i + -3ix + 2x + x2)(3i + x) = 0 Multiply (-6i + -3ix + 2x + x2) * (3i + x) x(-6i * (3i + x) + -3ix * (3i + x) + 2x * (3i + x) + x2(3i + x)) = 0 x((3i * -6i + x * -6i) + -3ix * (3i + x) + 2x * (3i + x) + x2(3i + x)) = 0 Reorder the terms: x((-6ix + -18i2) + -3ix * (3i + x) + 2x * (3i + x) + x2(3i + x)) = 0 x((-6ix + -18i2) + -3ix * (3i + x) + 2x * (3i + x) + x2(3i + x)) = 0 x(-6ix + -18i2 + (3i * -3ix + x * -3ix) + 2x * (3i + x) + x2(3i + x)) = 0 Reorder the terms: x(-6ix + -18i2 + (-3ix2 + -9i2x) + 2x * (3i + x) + x2(3i + x)) = 0 x(-6ix + -18i2 + (-3ix2 + -9i2x) + 2x * (3i + x) + x2(3i + x)) = 0 x(-6ix + -18i2 + -3ix2 + -9i2x + (3i * 2x + x * 2x) + x2(3i + x)) = 0 x(-6ix + -18i2 + -3ix2 + -9i2x + (6ix + 2x2) + x2(3i + x)) = 0 x(-6ix + -18i2 + -3ix2 + -9i2x + 6ix + 2x2 + (3i * x2 + x * x2)) = 0 x(-6ix + -18i2 + -3ix2 + -9i2x + 6ix + 2x2 + (3ix2 + x3)) = 0 Reorder the terms: x(-6ix + 6ix + -3ix2 + 3ix2 + -18i2 + -9i2x + 2x2 + x3) = 0 Combine like terms: -6ix + 6ix = 0 x(0 + -3ix2 + 3ix2 + -18i2 + -9i2x + 2x2 + x3) = 0 x(-3ix2 + 3ix2 + -18i2 + -9i2x + 2x2 + x3) = 0 Combine like terms: -3ix2 + 3ix2 = 0 x(0 + -18i2 + -9i2x + 2x2 + x3) = 0 x(-18i2 + -9i2x + 2x2 + x3) = 0 (-18i2 * x + -9i2x * x + 2x2 * x + x3 * x) = 0 (-18i2x + -9i2x2 + 2x3 + x4) = 0 Solving -18i2x + -9i2x2 + 2x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2x3' to each side of the equation. -18i2x + -9i2x2 + 2x3 + -2x3 + x4 = 0 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -18i2x + -9i2x2 + 0 + x4 = 0 + -2x3 -18i2x + -9i2x2 + x4 = 0 + -2x3 Remove the zero: -18i2x + -9i2x2 + x4 = -2x3 Add '-1x4' to each side of the equation. -18i2x + -9i2x2 + x4 + -1x4 = -2x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -18i2x + -9i2x2 + 0 = -2x3 + -1x4 -18i2x + -9i2x2 = -2x3 + -1x4 Reorder the terms: -18i2x + -9i2x2 + 2x3 + x4 = -2x3 + 2x3 + -1x4 + x4 Combine like terms: -2x3 + 2x3 = 0 -18i2x + -9i2x2 + 2x3 + x4 = 0 + -1x4 + x4 -18i2x + -9i2x2 + 2x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -18i2x + -9i2x2 + 2x3 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-18i2 + -9i2x + 2x2 + x3) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-18i2 + -9i2x + 2x2 + x3)' equal to zero and attempt to solve: Simplifying -18i2 + -9i2x + 2x2 + x3 = 0 Solving -18i2 + -9i2x + 2x2 + x3 = 0 Move all terms containing i to the left, all other terms to the right. Add '-2x2' to each side of the equation. -18i2 + -9i2x + 2x2 + -2x2 + x3 = 0 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -18i2 + -9i2x + 0 + x3 = 0 + -2x2 -18i2 + -9i2x + x3 = 0 + -2x2 Remove the zero: -18i2 + -9i2x + x3 = -2x2 Add '-1x3' to each side of the equation. -18i2 + -9i2x + x3 + -1x3 = -2x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -18i2 + -9i2x + 0 = -2x2 + -1x3 -18i2 + -9i2x = -2x2 + -1x3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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