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Simplifying 3(x + -1(4 + -3i))(x + -1(4 + 3i))(x)(x + -3) = 0 3(x + (4 * -1 + -3i * -1))(x + -1(4 + 3i))(x)(x + -3) = 0 3(x + (-4 + 3i))(x + -1(4 + 3i))(x)(x + -3) = 0 Reorder the terms: 3(-4 + 3i + x)(x + -1(4 + 3i))(x)(x + -3) = 0 3(-4 + 3i + x)(x + (4 * -1 + 3i * -1))(x)(x + -3) = 0 3(-4 + 3i + x)(x + (-4 + -3i))(x)(x + -3) = 0 Reorder the terms: 3(-4 + 3i + x)(-4 + -3i + x)(x)(x + -3) = 0 Reorder the terms: 3(-4 + 3i + x)(-4 + -3i + x) * x(-3 + x) = 0 Reorder the terms for easier multiplication: 3x(-4 + 3i + x)(-4 + -3i + x)(-3 + x) = 0 Multiply (-4 + 3i + x) * (-4 + -3i + x) 3x(-4(-4 + -3i + x) + 3i * (-4 + -3i + x) + x(-4 + -3i + x))(-3 + x) = 0 3x((-4 * -4 + -3i * -4 + x * -4) + 3i * (-4 + -3i + x) + x(-4 + -3i + x))(-3 + x) = 0 3x((16 + 12i + -4x) + 3i * (-4 + -3i + x) + x(-4 + -3i + x))(-3 + x) = 0 3x(16 + 12i + -4x + (-4 * 3i + -3i * 3i + x * 3i) + x(-4 + -3i + x))(-3 + x) = 0 Reorder the terms: 3x(16 + 12i + -4x + (-12i + 3ix + -9i2) + x(-4 + -3i + x))(-3 + x) = 0 3x(16 + 12i + -4x + (-12i + 3ix + -9i2) + x(-4 + -3i + x))(-3 + x) = 0 3x(16 + 12i + -4x + -12i + 3ix + -9i2 + (-4 * x + -3i * x + x * x))(-3 + x) = 0 Reorder the terms: 3x(16 + 12i + -4x + -12i + 3ix + -9i2 + (-3ix + -4x + x2))(-3 + x) = 0 3x(16 + 12i + -4x + -12i + 3ix + -9i2 + (-3ix + -4x + x2))(-3 + x) = 0 Reorder the terms: 3x(16 + 12i + -12i + 3ix + -3ix + -9i2 + -4x + -4x + x2)(-3 + x) = 0 Combine like terms: 12i + -12i = 0 3x(16 + 0 + 3ix + -3ix + -9i2 + -4x + -4x + x2)(-3 + x) = 0 3x(16 + 3ix + -3ix + -9i2 + -4x + -4x + x2)(-3 + x) = 0 Combine like terms: 3ix + -3ix = 0 3x(16 + 0 + -9i2 + -4x + -4x + x2)(-3 + x) = 0 3x(16 + -9i2 + -4x + -4x + x2)(-3 + x) = 0 Combine like terms: -4x + -4x = -8x 3x(16 + -9i2 + -8x + x2)(-3 + x) = 0 Multiply (16 + -9i2 + -8x + x2) * (-3 + x) 3x(16(-3 + x) + -9i2 * (-3 + x) + -8x * (-3 + x) + x2(-3 + x)) = 0 3x((-3 * 16 + x * 16) + -9i2 * (-3 + x) + -8x * (-3 + x) + x2(-3 + x)) = 0 3x((-48 + 16x) + -9i2 * (-3 + x) + -8x * (-3 + x) + x2(-3 + x)) = 0 3x(-48 + 16x + (-3 * -9i2 + x * -9i2) + -8x * (-3 + x) + x2(-3 + x)) = 0 3x(-48 + 16x + (27i2 + -9i2x) + -8x * (-3 + x) + x2(-3 + x)) = 0 3x(-48 + 16x + 27i2 + -9i2x + (-3 * -8x + x * -8x) + x2(-3 + x)) = 0 3x(-48 + 16x + 27i2 + -9i2x + (24x + -8x2) + x2(-3 + x)) = 0 3x(-48 + 16x + 27i2 + -9i2x + 24x + -8x2 + (-3 * x2 + x * x2)) = 0 3x(-48 + 16x + 27i2 + -9i2x + 24x + -8x2 + (-3x2 + x3)) = 0 Reorder the terms: 3x(-48 + 27i2 + -9i2x + 16x + 24x + -8x2 + -3x2 + x3) = 0 Combine like terms: 16x + 24x = 40x 3x(-48 + 27i2 + -9i2x + 40x + -8x2 + -3x2 + x3) = 0 Combine like terms: -8x2 + -3x2 = -11x2 3x(-48 + 27i2 + -9i2x + 40x + -11x2 + x3) = 0 (-48 * 3x + 27i2 * 3x + -9i2x * 3x + 40x * 3x + -11x2 * 3x + x3 * 3x) = 0 Reorder the terms: (81i2x + -27i2x2 + -144x + 120x2 + -33x3 + 3x4) = 0 (81i2x + -27i2x2 + -144x + 120x2 + -33x3 + 3x4) = 0 Solving 81i2x + -27i2x2 + -144x + 120x2 + -33x3 + 3x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '144x' to each side of the equation. 81i2x + -27i2x2 + -144x + 120x2 + -33x3 + 144x + 3x4 = 0 + 144x Reorder the terms: 81i2x + -27i2x2 + -144x + 144x + 120x2 + -33x3 + 3x4 = 0 + 144x Combine like terms: -144x + 144x = 0 81i2x + -27i2x2 + 0 + 120x2 + -33x3 + 3x4 = 0 + 144x 81i2x + -27i2x2 + 120x2 + -33x3 + 3x4 = 0 + 144x Remove the zero: 81i2x + -27i2x2 + 120x2 + -33x3 + 3x4 = 144x Add '-120x2' to each side of the equation. 81i2x + -27i2x2 + 120x2 + -33x3 + -120x2 + 3x4 = 144x + -120x2 Reorder the terms: 81i2x + -27i2x2 + 120x2 + -120x2 + -33x3 + 3x4 = 144x + -120x2 Combine like terms: 120x2 + -120x2 = 0 81i2x + -27i2x2 + 0 + -33x3 + 3x4 = 144x + -120x2 81i2x + -27i2x2 + -33x3 + 3x4 = 144x + -120x2 Add '33x3' to each side of the equation. 81i2x + -27i2x2 + -33x3 + 33x3 + 3x4 = 144x + -120x2 + 33x3 Combine like terms: -33x3 + 33x3 = 0 81i2x + -27i2x2 + 0 + 3x4 = 144x + -120x2 + 33x3 81i2x + -27i2x2 + 3x4 = 144x + -120x2 + 33x3 Add '-3x4' to each side of the equation. 81i2x + -27i2x2 + 3x4 + -3x4 = 144x + -120x2 + 33x3 + -3x4 Combine like terms: 3x4 + -3x4 = 0 81i2x + -27i2x2 + 0 = 144x + -120x2 + 33x3 + -3x4 81i2x + -27i2x2 = 144x + -120x2 + 33x3 + -3x4 Reorder the terms: 81i2x + -27i2x2 + -144x + 120x2 + -33x3 + 3x4 = 144x + -144x + -120x2 + 120x2 + 33x3 + -33x3 + -3x4 + 3x4 Combine like terms: 144x + -144x = 0 81i2x + -27i2x2 + -144x + 120x2 + -33x3 + 3x4 = 0 + -120x2 + 120x2 + 33x3 + -33x3 + -3x4 + 3x4 81i2x + -27i2x2 + -144x + 120x2 + -33x3 + 3x4 = -120x2 + 120x2 + 33x3 + -33x3 + -3x4 + 3x4 Combine like terms: -120x2 + 120x2 = 0 81i2x + -27i2x2 + -144x + 120x2 + -33x3 + 3x4 = 0 + 33x3 + -33x3 + -3x4 + 3x4 81i2x + -27i2x2 + -144x + 120x2 + -33x3 + 3x4 = 33x3 + -33x3 + -3x4 + 3x4 Combine like terms: 33x3 + -33x3 = 0 81i2x + -27i2x2 + -144x + 120x2 + -33x3 + 3x4 = 0 + -3x4 + 3x4 81i2x + -27i2x2 + -144x + 120x2 + -33x3 + 3x4 = -3x4 + 3x4 Combine like terms: -3x4 + 3x4 = 0 81i2x + -27i2x2 + -144x + 120x2 + -33x3 + 3x4 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(27i2 + -9i2x + -48 + 40x + -11x2 + x3) = 0 Ignore the factor 3.Subproblem 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 '(27i2 + -9i2x + -48 + 40x + -11x2 + x3)' equal to zero and attempt to solve: Simplifying 27i2 + -9i2x + -48 + 40x + -11x2 + x3 = 0 Reorder the terms: -48 + 27i2 + -9i2x + 40x + -11x2 + x3 = 0 Solving -48 + 27i2 + -9i2x + 40x + -11x2 + x3 = 0 Move all terms containing i to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 27i2 + -9i2x + 40x + -11x2 + 48 + x3 = 0 + 48 Reorder the terms: -48 + 48 + 27i2 + -9i2x + 40x + -11x2 + x3 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 27i2 + -9i2x + 40x + -11x2 + x3 = 0 + 48 27i2 + -9i2x + 40x + -11x2 + x3 = 0 + 48 Combine like terms: 0 + 48 = 48 27i2 + -9i2x + 40x + -11x2 + x3 = 48 Add '-40x' to each side of the equation. 27i2 + -9i2x + 40x + -11x2 + -40x + x3 = 48 + -40x Reorder the terms: 27i2 + -9i2x + 40x + -40x + -11x2 + x3 = 48 + -40x Combine like terms: 40x + -40x = 0 27i2 + -9i2x + 0 + -11x2 + x3 = 48 + -40x 27i2 + -9i2x + -11x2 + x3 = 48 + -40x Add '11x2' to each side of the equation. 27i2 + -9i2x + -11x2 + 11x2 + x3 = 48 + -40x + 11x2 Combine like terms: -11x2 + 11x2 = 0 27i2 + -9i2x + 0 + x3 = 48 + -40x + 11x2 27i2 + -9i2x + x3 = 48 + -40x + 11x2 Add '-1x3' to each side of the equation. 27i2 + -9i2x + x3 + -1x3 = 48 + -40x + 11x2 + -1x3 Combine like terms: x3 + -1x3 = 0 27i2 + -9i2x + 0 = 48 + -40x + 11x2 + -1x3 27i2 + -9i2x = 48 + -40x + 11x2 + -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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