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Simplifying -3(x + -3)(x + 2 + -4i)(x + 2 + 4i) = 0 Reorder the terms: -3(-3 + x)(x + 2 + -4i)(x + 2 + 4i) = 0 Reorder the terms: -3(-3 + x)(2 + -4i + x)(x + 2 + 4i) = 0 Reorder the terms: -3(-3 + x)(2 + -4i + x)(2 + 4i + x) = 0 Multiply (-3 + x) * (2 + -4i + x) -3(-3(2 + -4i + x) + x(2 + -4i + x))(2 + 4i + x) = 0 -3((2 * -3 + -4i * -3 + x * -3) + x(2 + -4i + x))(2 + 4i + x) = 0 -3((-6 + 12i + -3x) + x(2 + -4i + x))(2 + 4i + x) = 0 -3(-6 + 12i + -3x + (2 * x + -4i * x + x * x))(2 + 4i + x) = 0 Reorder the terms: -3(-6 + 12i + -3x + (-4ix + 2x + x2))(2 + 4i + x) = 0 -3(-6 + 12i + -3x + (-4ix + 2x + x2))(2 + 4i + x) = 0 Reorder the terms: -3(-6 + 12i + -4ix + -3x + 2x + x2)(2 + 4i + x) = 0 Combine like terms: -3x + 2x = -1x -3(-6 + 12i + -4ix + -1x + x2)(2 + 4i + x) = 0 Multiply (-6 + 12i + -4ix + -1x + x2) * (2 + 4i + x) -3(-6(2 + 4i + x) + 12i * (2 + 4i + x) + -4ix * (2 + 4i + x) + -1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0 -3((2 * -6 + 4i * -6 + x * -6) + 12i * (2 + 4i + x) + -4ix * (2 + 4i + x) + -1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0 -3((-12 + -24i + -6x) + 12i * (2 + 4i + x) + -4ix * (2 + 4i + x) + -1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0 -3(-12 + -24i + -6x + (2 * 12i + 4i * 12i + x * 12i) + -4ix * (2 + 4i + x) + -1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0 Reorder the terms: -3(-12 + -24i + -6x + (24i + 12ix + 48i2) + -4ix * (2 + 4i + x) + -1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0 -3(-12 + -24i + -6x + (24i + 12ix + 48i2) + -4ix * (2 + 4i + x) + -1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0 -3(-12 + -24i + -6x + 24i + 12ix + 48i2 + (2 * -4ix + 4i * -4ix + x * -4ix) + -1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0 Reorder the terms: -3(-12 + -24i + -6x + 24i + 12ix + 48i2 + (-8ix + -4ix2 + -16i2x) + -1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0 -3(-12 + -24i + -6x + 24i + 12ix + 48i2 + (-8ix + -4ix2 + -16i2x) + -1x * (2 + 4i + x) + x2(2 + 4i + x)) = 0 -3(-12 + -24i + -6x + 24i + 12ix + 48i2 + -8ix + -4ix2 + -16i2x + (2 * -1x + 4i * -1x + x * -1x) + x2(2 + 4i + x)) = 0 Reorder the terms: -3(-12 + -24i + -6x + 24i + 12ix + 48i2 + -8ix + -4ix2 + -16i2x + (-4ix + -2x + -1x2) + x2(2 + 4i + x)) = 0 -3(-12 + -24i + -6x + 24i + 12ix + 48i2 + -8ix + -4ix2 + -16i2x + (-4ix + -2x + -1x2) + x2(2 + 4i + x)) = 0 -3(-12 + -24i + -6x + 24i + 12ix + 48i2 + -8ix + -4ix2 + -16i2x + -4ix + -2x + -1x2 + (2 * x2 + 4i * x2 + x * x2)) = 0 Reorder the terms: -3(-12 + -24i + -6x + 24i + 12ix + 48i2 + -8ix + -4ix2 + -16i2x + -4ix + -2x + -1x2 + (4ix2 + 2x2 + x3)) = 0 -3(-12 + -24i + -6x + 24i + 12ix + 48i2 + -8ix + -4ix2 + -16i2x + -4ix + -2x + -1x2 + (4ix2 + 2x2 + x3)) = 0 Reorder the terms: -3(-12 + -24i + 24i + 12ix + -8ix + -4ix + -4ix2 + 4ix2 + 48i2 + -16i2x + -6x + -2x + -1x2 + 2x2 + x3) = 0 Combine like terms: -24i + 24i = 0 -3(-12 + 0 + 12ix + -8ix + -4ix + -4ix2 + 4ix2 + 48i2 + -16i2x + -6x + -2x + -1x2 + 2x2 + x3) = 0 -3(-12 + 12ix + -8ix + -4ix + -4ix2 + 4ix2 + 48i2 + -16i2x + -6x + -2x + -1x2 + 2x2 + x3) = 0 Combine like terms: 12ix + -8ix = 4ix -3(-12 + 4ix + -4ix + -4ix2 + 4ix2 + 48i2 + -16i2x + -6x + -2x + -1x2 + 2x2 + x3) = 0 Combine like terms: 4ix + -4ix = 0 -3(-12 + 0 + -4ix2 + 4ix2 + 48i2 + -16i2x + -6x + -2x + -1x2 + 2x2 + x3) = 0 -3(-12 + -4ix2 + 4ix2 + 48i2 + -16i2x + -6x + -2x + -1x2 + 2x2 + x3) = 0 Combine like terms: -4ix2 + 4ix2 = 0 -3(-12 + 0 + 48i2 + -16i2x + -6x + -2x + -1x2 + 2x2 + x3) = 0 -3(-12 + 48i2 + -16i2x + -6x + -2x + -1x2 + 2x2 + x3) = 0 Combine like terms: -6x + -2x = -8x -3(-12 + 48i2 + -16i2x + -8x + -1x2 + 2x2 + x3) = 0 Combine like terms: -1x2 + 2x2 = 1x2 -3(-12 + 48i2 + -16i2x + -8x + 1x2 + x3) = 0 (-12 * -3 + 48i2 * -3 + -16i2x * -3 + -8x * -3 + 1x2 * -3 + x3 * -3) = 0 (36 + -144i2 + 48i2x + 24x + -3x2 + -3x3) = 0 Solving 36 + -144i2 + 48i2x + 24x + -3x2 + -3x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -144i2 + 48i2x + 24x + -3x2 + -36 + -3x3 = 0 + -36 Reorder the terms: 36 + -36 + -144i2 + 48i2x + 24x + -3x2 + -3x3 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -144i2 + 48i2x + 24x + -3x2 + -3x3 = 0 + -36 -144i2 + 48i2x + 24x + -3x2 + -3x3 = 0 + -36 Combine like terms: 0 + -36 = -36 -144i2 + 48i2x + 24x + -3x2 + -3x3 = -36 Add '-24x' to each side of the equation. -144i2 + 48i2x + 24x + -3x2 + -24x + -3x3 = -36 + -24x Reorder the terms: -144i2 + 48i2x + 24x + -24x + -3x2 + -3x3 = -36 + -24x Combine like terms: 24x + -24x = 0 -144i2 + 48i2x + 0 + -3x2 + -3x3 = -36 + -24x -144i2 + 48i2x + -3x2 + -3x3 = -36 + -24x Add '3x2' to each side of the equation. -144i2 + 48i2x + -3x2 + 3x2 + -3x3 = -36 + -24x + 3x2 Combine like terms: -3x2 + 3x2 = 0 -144i2 + 48i2x + 0 + -3x3 = -36 + -24x + 3x2 -144i2 + 48i2x + -3x3 = -36 + -24x + 3x2 Add '3x3' to each side of the equation. -144i2 + 48i2x + -3x3 + 3x3 = -36 + -24x + 3x2 + 3x3 Combine like terms: -3x3 + 3x3 = 0 -144i2 + 48i2x + 0 = -36 + -24x + 3x2 + 3x3 -144i2 + 48i2x = -36 + -24x + 3x2 + 3x3 Reorder the terms: 36 + -144i2 + 48i2x + 24x + -3x2 + -3x3 = -36 + -24x + 3x2 + 3x3 + 36 + 24x + -3x2 + -3x3 Reorder the terms: 36 + -144i2 + 48i2x + 24x + -3x2 + -3x3 = -36 + 36 + -24x + 24x + 3x2 + -3x2 + 3x3 + -3x3 Combine like terms: -36 + 36 = 0 36 + -144i2 + 48i2x + 24x + -3x2 + -3x3 = 0 + -24x + 24x + 3x2 + -3x2 + 3x3 + -3x3 36 + -144i2 + 48i2x + 24x + -3x2 + -3x3 = -24x + 24x + 3x2 + -3x2 + 3x3 + -3x3 Combine like terms: -24x + 24x = 0 36 + -144i2 + 48i2x + 24x + -3x2 + -3x3 = 0 + 3x2 + -3x2 + 3x3 + -3x3 36 + -144i2 + 48i2x + 24x + -3x2 + -3x3 = 3x2 + -3x2 + 3x3 + -3x3 Combine like terms: 3x2 + -3x2 = 0 36 + -144i2 + 48i2x + 24x + -3x2 + -3x3 = 0 + 3x3 + -3x3 36 + -144i2 + 48i2x + 24x + -3x2 + -3x3 = 3x3 + -3x3 Combine like terms: 3x3 + -3x3 = 0 36 + -144i2 + 48i2x + 24x + -3x2 + -3x3 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(12 + -48i2 + 16i2x + 8x + -1x2 + -1x3) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(12 + -48i2 + 16i2x + 8x + -1x2 + -1x3)' equal to zero and attempt to solve: Simplifying 12 + -48i2 + 16i2x + 8x + -1x2 + -1x3 = 0 Solving 12 + -48i2 + 16i2x + 8x + -1x2 + -1x3 = 0 Move all terms containing i to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -48i2 + 16i2x + 8x + -1x2 + -12 + -1x3 = 0 + -12 Reorder the terms: 12 + -12 + -48i2 + 16i2x + 8x + -1x2 + -1x3 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -48i2 + 16i2x + 8x + -1x2 + -1x3 = 0 + -12 -48i2 + 16i2x + 8x + -1x2 + -1x3 = 0 + -12 Combine like terms: 0 + -12 = -12 -48i2 + 16i2x + 8x + -1x2 + -1x3 = -12 Add '-8x' to each side of the equation. -48i2 + 16i2x + 8x + -1x2 + -8x + -1x3 = -12 + -8x Reorder the terms: -48i2 + 16i2x + 8x + -8x + -1x2 + -1x3 = -12 + -8x Combine like terms: 8x + -8x = 0 -48i2 + 16i2x + 0 + -1x2 + -1x3 = -12 + -8x -48i2 + 16i2x + -1x2 + -1x3 = -12 + -8x Add 'x2' to each side of the equation. -48i2 + 16i2x + -1x2 + x2 + -1x3 = -12 + -8x + x2 Combine like terms: -1x2 + x2 = 0 -48i2 + 16i2x + 0 + -1x3 = -12 + -8x + x2 -48i2 + 16i2x + -1x3 = -12 + -8x + x2 Add 'x3' to each side of the equation. -48i2 + 16i2x + -1x3 + x3 = -12 + -8x + x2 + x3 Combine like terms: -1x3 + x3 = 0 -48i2 + 16i2x + 0 = -12 + -8x + x2 + x3 -48i2 + 16i2x = -12 + -8x + x2 + x3 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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