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Simplifying z(1 + 3i) + -5(1 + 3i) = 2z (1 * z + 3i * z) + -5(1 + 3i) = 2z Reorder the terms: (3iz + 1z) + -5(1 + 3i) = 2z (3iz + 1z) + -5(1 + 3i) = 2z 3iz + 1z + (1 * -5 + 3i * -5) = 2z 3iz + 1z + (-5 + -15i) = 2z Reorder the terms: -5 + -15i + 3iz + 1z = 2z Solving -5 + -15i + 3iz + 1z = 2z Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '5' to each side of the equation. -5 + -15i + 3iz + 5 + 1z = 5 + 2z Reorder the terms: -5 + 5 + -15i + 3iz + 1z = 5 + 2z Combine like terms: -5 + 5 = 0 0 + -15i + 3iz + 1z = 5 + 2z -15i + 3iz + 1z = 5 + 2z Add '-1z' to each side of the equation. -15i + 3iz + 1z + -1z = 5 + 2z + -1z Combine like terms: 1z + -1z = 0 -15i + 3iz + 0 = 5 + 2z + -1z -15i + 3iz = 5 + 2z + -1z Combine like terms: 2z + -1z = 1z -15i + 3iz = 5 + 1z Reorder the terms: -5 + -15i + 3iz + -1z = 5 + 1z + -5 + -1z Reorder the terms: -5 + -15i + 3iz + -1z = 5 + -5 + 1z + -1z Combine like terms: 5 + -5 = 0 -5 + -15i + 3iz + -1z = 0 + 1z + -1z -5 + -15i + 3iz + -1z = 1z + -1z Combine like terms: 1z + -1z = 0 -5 + -15i + 3iz + -1z = 0 The solution to this equation could not be determined.
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