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Simplifying 3(((z + 1)(z + -2))(z + 2I))(z + -2I) = 0 Reorder the terms: 3(((1 + z)(z + -2))(z + 2I))(z + -2I) = 0 Reorder the terms: 3(((1 + z)(-2 + z))(z + 2I))(z + -2I) = 0 Multiply (1 + z) * (-2 + z) 3(((1(-2 + z) + z(-2 + z)))(z + 2I))(z + -2I) = 0 3((((-2 * 1 + z * 1) + z(-2 + z)))(z + 2I))(z + -2I) = 0 3((((-2 + 1z) + z(-2 + z)))(z + 2I))(z + -2I) = 0 3(((-2 + 1z + (-2 * z + z * z)))(z + 2I))(z + -2I) = 0 3(((-2 + 1z + (-2z + z2)))(z + 2I))(z + -2I) = 0 Combine like terms: 1z + -2z = -1z 3(((-2 + -1z + z2))(z + 2I))(z + -2I) = 0 Reorder the terms: 3((-2 + -1z + z2)(2I + z))(z + -2I) = 0 Multiply (-2 + -1z + z2) * (2I + z) 3((-2(2I + z) + -1z * (2I + z) + z2(2I + z)))(z + -2I) = 0 3(((2I * -2 + z * -2) + -1z * (2I + z) + z2(2I + z)))(z + -2I) = 0 3(((-4I + -2z) + -1z * (2I + z) + z2(2I + z)))(z + -2I) = 0 3((-4I + -2z + (2I * -1z + z * -1z) + z2(2I + z)))(z + -2I) = 0 3((-4I + -2z + (-2zI + -1z2) + z2(2I + z)))(z + -2I) = 0 3((-4I + -2z + -2zI + -1z2 + (2I * z2 + z * z2)))(z + -2I) = 0 3((-4I + -2z + -2zI + -1z2 + (2z2I + z3)))(z + -2I) = 0 3((-4I + -2z + -2zI + -1z2 + 2z2I + z3))(z + -2I) = 0 Reorder the terms: 3(-4I + -2z + -2zI + -1z2 + 2z2I + z3)(-2I + z) = 0 Multiply (-4I + -2z + -2zI + -1z2 + 2z2I + z3) * (-2I + z) 3(-4I * (-2I + z) + -2z * (-2I + z) + -2zI * (-2I + z) + -1z2 * (-2I + z) + 2z2I * (-2I + z) + z3(-2I + z)) = 0 3((-2I * -4I + z * -4I) + -2z * (-2I + z) + -2zI * (-2I + z) + -1z2 * (-2I + z) + 2z2I * (-2I + z) + z3(-2I + z)) = 0 3((8I2 + -4zI) + -2z * (-2I + z) + -2zI * (-2I + z) + -1z2 * (-2I + z) + 2z2I * (-2I + z) + z3(-2I + z)) = 0 3(8I2 + -4zI + (-2I * -2z + z * -2z) + -2zI * (-2I + z) + -1z2 * (-2I + z) + 2z2I * (-2I + z) + z3(-2I + z)) = 0 3(8I2 + -4zI + (4zI + -2z2) + -2zI * (-2I + z) + -1z2 * (-2I + z) + 2z2I * (-2I + z) + z3(-2I + z)) = 0 3(8I2 + -4zI + 4zI + -2z2 + (-2I * -2zI + z * -2zI) + -1z2 * (-2I + z) + 2z2I * (-2I + z) + z3(-2I + z)) = 0 3(8I2 + -4zI + 4zI + -2z2 + (4zI2 + -2z2I) + -1z2 * (-2I + z) + 2z2I * (-2I + z) + z3(-2I + z)) = 0 3(8I2 + -4zI + 4zI + -2z2 + 4zI2 + -2z2I + (-2I * -1z2 + z * -1z2) + 2z2I * (-2I + z) + z3(-2I + z)) = 0 3(8I2 + -4zI + 4zI + -2z2 + 4zI2 + -2z2I + (2z2I + -1z3) + 2z2I * (-2I + z) + z3(-2I + z)) = 0 3(8I2 + -4zI + 4zI + -2z2 + 4zI2 + -2z2I + 2z2I + -1z3 + (-2I * 2z2I + z * 2z2I) + z3(-2I + z)) = 0 3(8I2 + -4zI + 4zI + -2z2 + 4zI2 + -2z2I + 2z2I + -1z3 + (-4z2I2 + 2z3I) + z3(-2I + z)) = 0 3(8I2 + -4zI + 4zI + -2z2 + 4zI2 + -2z2I + 2z2I + -1z3 + -4z2I2 + 2z3I + (-2I * z3 + z * z3)) = 0 3(8I2 + -4zI + 4zI + -2z2 + 4zI2 + -2z2I + 2z2I + -1z3 + -4z2I2 + 2z3I + (-2z3I + z4)) = 0 Reorder the terms: 3(8I2 + -4zI + 4zI + 4zI2 + -2z2 + -2z2I + 2z2I + -4z2I2 + -1z3 + 2z3I + -2z3I + z4) = 0 Combine like terms: -4zI + 4zI = 0 3(8I2 + 0 + 4zI2 + -2z2 + -2z2I + 2z2I + -4z2I2 + -1z3 + 2z3I + -2z3I + z4) = 0 3(8I2 + 4zI2 + -2z2 + -2z2I + 2z2I + -4z2I2 + -1z3 + 2z3I + -2z3I + z4) = 0 Combine like terms: -2z2I + 2z2I = 0 3(8I2 + 4zI2 + -2z2 + 0 + -4z2I2 + -1z3 + 2z3I + -2z3I + z4) = 0 3(8I2 + 4zI2 + -2z2 + -4z2I2 + -1z3 + 2z3I + -2z3I + z4) = 0 Combine like terms: 2z3I + -2z3I = 0 3(8I2 + 4zI2 + -2z2 + -4z2I2 + -1z3 + 0 + z4) = 0 3(8I2 + 4zI2 + -2z2 + -4z2I2 + -1z3 + z4) = 0 (8I2 * 3 + 4zI2 * 3 + -2z2 * 3 + -4z2I2 * 3 + -1z3 * 3 + z4 * 3) = 0 (24I2 + 12zI2 + -6z2 + -12z2I2 + -3z3 + 3z4) = 0 Solving 24I2 + 12zI2 + -6z2 + -12z2I2 + -3z3 + 3z4 = 0 Solving for variable 'I'. Move all terms containing I to the left, all other terms to the right. Add '6z2' to each side of the equation. 24I2 + 12zI2 + -6z2 + -12z2I2 + -3z3 + 6z2 + 3z4 = 0 + 6z2 Reorder the terms: 24I2 + 12zI2 + -6z2 + 6z2 + -12z2I2 + -3z3 + 3z4 = 0 + 6z2 Combine like terms: -6z2 + 6z2 = 0 24I2 + 12zI2 + 0 + -12z2I2 + -3z3 + 3z4 = 0 + 6z2 24I2 + 12zI2 + -12z2I2 + -3z3 + 3z4 = 0 + 6z2 Remove the zero: 24I2 + 12zI2 + -12z2I2 + -3z3 + 3z4 = 6z2 Add '3z3' to each side of the equation. 24I2 + 12zI2 + -12z2I2 + -3z3 + 3z3 + 3z4 = 6z2 + 3z3 Combine like terms: -3z3 + 3z3 = 0 24I2 + 12zI2 + -12z2I2 + 0 + 3z4 = 6z2 + 3z3 24I2 + 12zI2 + -12z2I2 + 3z4 = 6z2 + 3z3 Add '-3z4' to each side of the equation. 24I2 + 12zI2 + -12z2I2 + 3z4 + -3z4 = 6z2 + 3z3 + -3z4 Combine like terms: 3z4 + -3z4 = 0 24I2 + 12zI2 + -12z2I2 + 0 = 6z2 + 3z3 + -3z4 24I2 + 12zI2 + -12z2I2 = 6z2 + 3z3 + -3z4 Reorder the terms: 24I2 + 12zI2 + -6z2 + -12z2I2 + -3z3 + 3z4 = 6z2 + 3z3 + -3z4 + -6z2 + -3z3 + 3z4 Reorder the terms: 24I2 + 12zI2 + -6z2 + -12z2I2 + -3z3 + 3z4 = 6z2 + -6z2 + 3z3 + -3z3 + -3z4 + 3z4 Combine like terms: 6z2 + -6z2 = 0 24I2 + 12zI2 + -6z2 + -12z2I2 + -3z3 + 3z4 = 0 + 3z3 + -3z3 + -3z4 + 3z4 24I2 + 12zI2 + -6z2 + -12z2I2 + -3z3 + 3z4 = 3z3 + -3z3 + -3z4 + 3z4 Combine like terms: 3z3 + -3z3 = 0 24I2 + 12zI2 + -6z2 + -12z2I2 + -3z3 + 3z4 = 0 + -3z4 + 3z4 24I2 + 12zI2 + -6z2 + -12z2I2 + -3z3 + 3z4 = -3z4 + 3z4 Combine like terms: -3z4 + 3z4 = 0 24I2 + 12zI2 + -6z2 + -12z2I2 + -3z3 + 3z4 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(8I2 + 4zI2 + -2z2 + -4z2I2 + -1z3 + z4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8I2 + 4zI2 + -2z2 + -4z2I2 + -1z3 + z4)' equal to zero and attempt to solve: Simplifying 8I2 + 4zI2 + -2z2 + -4z2I2 + -1z3 + z4 = 0 Solving 8I2 + 4zI2 + -2z2 + -4z2I2 + -1z3 + z4 = 0 Move all terms containing I to the left, all other terms to the right. Add '2z2' to each side of the equation. 8I2 + 4zI2 + -2z2 + -4z2I2 + -1z3 + 2z2 + z4 = 0 + 2z2 Reorder the terms: 8I2 + 4zI2 + -2z2 + 2z2 + -4z2I2 + -1z3 + z4 = 0 + 2z2 Combine like terms: -2z2 + 2z2 = 0 8I2 + 4zI2 + 0 + -4z2I2 + -1z3 + z4 = 0 + 2z2 8I2 + 4zI2 + -4z2I2 + -1z3 + z4 = 0 + 2z2 Remove the zero: 8I2 + 4zI2 + -4z2I2 + -1z3 + z4 = 2z2 Add 'z3' to each side of the equation. 8I2 + 4zI2 + -4z2I2 + -1z3 + z3 + z4 = 2z2 + z3 Combine like terms: -1z3 + z3 = 0 8I2 + 4zI2 + -4z2I2 + 0 + z4 = 2z2 + z3 8I2 + 4zI2 + -4z2I2 + z4 = 2z2 + z3 Add '-1z4' to each side of the equation. 8I2 + 4zI2 + -4z2I2 + z4 + -1z4 = 2z2 + z3 + -1z4 Combine like terms: z4 + -1z4 = 0 8I2 + 4zI2 + -4z2I2 + 0 = 2z2 + z3 + -1z4 8I2 + 4zI2 + -4z2I2 = 2z2 + z3 + -1z4 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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