z^3-3z^2+(1+3i)z-6i+a=0

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Solution for z^3-3z^2+(1+3i)z-6i+a=0 equation: 


Simplifying
z3 + -3z2 + (1 + 3i) * z + -6i + a = 0

Reorder the terms for easier multiplication:
z3 + -3z2 + z(1 + 3i) + -6i + a = 0
z3 + -3z2 + (1 * z + 3i * z) + -6i + a = 0

Reorder the terms:
z3 + -3z2 + (3iz + 1z) + -6i + a = 0
z3 + -3z2 + (3iz + 1z) + -6i + a = 0

Reorder the terms:
a + -6i + 3iz + 1z + -3z2 + z3 = 0

Solving
a + -6i + 3iz + 1z + -3z2 + z3 = 0

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '6i' to each side of the equation.
a + -6i + 3iz + 1z + -3z2 + 6i + z3 = 0 + 6i

Reorder the terms:
a + -6i + 6i + 3iz + 1z + -3z2 + z3 = 0 + 6i

Combine like terms: -6i + 6i = 0
a + 0 + 3iz + 1z + -3z2 + z3 = 0 + 6i
a + 3iz + 1z + -3z2 + z3 = 0 + 6i
Remove the zero:
a + 3iz + 1z + -3z2 + z3 = 6i

Add '-3iz' to each side of the equation.
a + 3iz + 1z + -3z2 + -3iz + z3 = 6i + -3iz

Reorder the terms:
a + 3iz + -3iz + 1z + -3z2 + z3 = 6i + -3iz

Combine like terms: 3iz + -3iz = 0
a + 0 + 1z + -3z2 + z3 = 6i + -3iz
a + 1z + -3z2 + z3 = 6i + -3iz

Add '-1z' to each side of the equation.
a + 1z + -3z2 + -1z + z3 = 6i + -3iz + -1z

Reorder the terms:
a + 1z + -1z + -3z2 + z3 = 6i + -3iz + -1z

Combine like terms: 1z + -1z = 0
a + 0 + -3z2 + z3 = 6i + -3iz + -1z
a + -3z2 + z3 = 6i + -3iz + -1z

Add '3z2' to each side of the equation.
a + -3z2 + 3z2 + z3 = 6i + -3iz + -1z + 3z2

Combine like terms: -3z2 + 3z2 = 0
a + 0 + z3 = 6i + -3iz + -1z + 3z2
a + z3 = 6i + -3iz + -1z + 3z2

Add '-1z3' to each side of the equation.
a + z3 + -1z3 = 6i + -3iz + -1z + 3z2 + -1z3

Combine like terms: z3 + -1z3 = 0
a + 0 = 6i + -3iz + -1z + 3z2 + -1z3
a = 6i + -3iz + -1z + 3z2 + -1z3

Simplifying
a = 6i + -3iz + -1z + 3z2 + -1z3

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