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Simplifying 2z2 + (12 + 8i) * z + -40 + 24i = 0 Reorder the terms for easier multiplication: 2z2 + z(12 + 8i) + -40 + 24i = 0 2z2 + (12 * z + 8i * z) + -40 + 24i = 0 Reorder the terms: 2z2 + (8iz + 12z) + -40 + 24i = 0 2z2 + (8iz + 12z) + -40 + 24i = 0 Reorder the terms: -40 + 24i + 8iz + 12z + 2z2 = 0 Solving -40 + 24i + 8iz + 12z + 2z2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 24i + 8iz + 12z + 40 + 2z2 = 0 + 40 Reorder the terms: -40 + 40 + 24i + 8iz + 12z + 2z2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 24i + 8iz + 12z + 2z2 = 0 + 40 24i + 8iz + 12z + 2z2 = 0 + 40 Combine like terms: 0 + 40 = 40 24i + 8iz + 12z + 2z2 = 40 Add '-12z' to each side of the equation. 24i + 8iz + 12z + -12z + 2z2 = 40 + -12z Combine like terms: 12z + -12z = 0 24i + 8iz + 0 + 2z2 = 40 + -12z 24i + 8iz + 2z2 = 40 + -12z Add '-2z2' to each side of the equation. 24i + 8iz + 2z2 + -2z2 = 40 + -12z + -2z2 Combine like terms: 2z2 + -2z2 = 0 24i + 8iz + 0 = 40 + -12z + -2z2 24i + 8iz = 40 + -12z + -2z2 Reorder the terms: -40 + 24i + 8iz + 12z + 2z2 = 40 + -12z + -2z2 + -40 + 12z + 2z2 Reorder the terms: -40 + 24i + 8iz + 12z + 2z2 = 40 + -40 + -12z + 12z + -2z2 + 2z2 Combine like terms: 40 + -40 = 0 -40 + 24i + 8iz + 12z + 2z2 = 0 + -12z + 12z + -2z2 + 2z2 -40 + 24i + 8iz + 12z + 2z2 = -12z + 12z + -2z2 + 2z2 Combine like terms: -12z + 12z = 0 -40 + 24i + 8iz + 12z + 2z2 = 0 + -2z2 + 2z2 -40 + 24i + 8iz + 12z + 2z2 = -2z2 + 2z2 Combine like terms: -2z2 + 2z2 = 0 -40 + 24i + 8iz + 12z + 2z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 12i + 4iz + 6z + z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + 12i + 4iz + 6z + z2)' equal to zero and attempt to solve: Simplifying -20 + 12i + 4iz + 6z + z2 = 0 Solving -20 + 12i + 4iz + 6z + z2 = 0 Move all terms containing i to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 12i + 4iz + 6z + 20 + z2 = 0 + 20 Reorder the terms: -20 + 20 + 12i + 4iz + 6z + z2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 12i + 4iz + 6z + z2 = 0 + 20 12i + 4iz + 6z + z2 = 0 + 20 Combine like terms: 0 + 20 = 20 12i + 4iz + 6z + z2 = 20 Add '-6z' to each side of the equation. 12i + 4iz + 6z + -6z + z2 = 20 + -6z Combine like terms: 6z + -6z = 0 12i + 4iz + 0 + z2 = 20 + -6z 12i + 4iz + z2 = 20 + -6z Add '-1z2' to each side of the equation. 12i + 4iz + z2 + -1z2 = 20 + -6z + -1z2 Combine like terms: z2 + -1z2 = 0 12i + 4iz + 0 = 20 + -6z + -1z2 12i + 4iz = 20 + -6z + -1z2 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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