4z^2+4(1+3i)z-3(5+6i)=0

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Solution for 4z^2+4(1+3i)z-3(5+6i)=0 equation: 


Simplifying
4z2 + 4(1 + 3i) * z + -3(5 + 6i) = 0

Reorder the terms for easier multiplication:
4z2 + 4z(1 + 3i) + -3(5 + 6i) = 0
4z2 + (1 * 4z + 3i * 4z) + -3(5 + 6i) = 0

Reorder the terms:
4z2 + (12iz + 4z) + -3(5 + 6i) = 0
4z2 + (12iz + 4z) + -3(5 + 6i) = 0
4z2 + 12iz + 4z + (5 * -3 + 6i * -3) = 0
4z2 + 12iz + 4z + (-15 + -18i) = 0

Reorder the terms:
-15 + -18i + 12iz + 4z + 4z2 = 0

Solving
-15 + -18i + 12iz + 4z + 4z2 = 0

Solving for variable 'i'.

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

Add '15' to each side of the equation.
-15 + -18i + 12iz + 4z + 15 + 4z2 = 0 + 15

Reorder the terms:
-15 + 15 + -18i + 12iz + 4z + 4z2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -18i + 12iz + 4z + 4z2 = 0 + 15
-18i + 12iz + 4z + 4z2 = 0 + 15

Combine like terms: 0 + 15 = 15
-18i + 12iz + 4z + 4z2 = 15

Add '-4z' to each side of the equation.
-18i + 12iz + 4z + -4z + 4z2 = 15 + -4z

Combine like terms: 4z + -4z = 0
-18i + 12iz + 0 + 4z2 = 15 + -4z
-18i + 12iz + 4z2 = 15 + -4z

Add '-4z2' to each side of the equation.
-18i + 12iz + 4z2 + -4z2 = 15 + -4z + -4z2

Combine like terms: 4z2 + -4z2 = 0
-18i + 12iz + 0 = 15 + -4z + -4z2
-18i + 12iz = 15 + -4z + -4z2

Reorder the terms:
-15 + -18i + 12iz + 4z + 4z2 = 15 + -4z + -4z2 + -15 + 4z + 4z2

Reorder the terms:
-15 + -18i + 12iz + 4z + 4z2 = 15 + -15 + -4z + 4z + -4z2 + 4z2

Combine like terms: 15 + -15 = 0
-15 + -18i + 12iz + 4z + 4z2 = 0 + -4z + 4z + -4z2 + 4z2
-15 + -18i + 12iz + 4z + 4z2 = -4z + 4z + -4z2 + 4z2

Combine like terms: -4z + 4z = 0
-15 + -18i + 12iz + 4z + 4z2 = 0 + -4z2 + 4z2
-15 + -18i + 12iz + 4z + 4z2 = -4z2 + 4z2

Combine like terms: -4z2 + 4z2 = 0
-15 + -18i + 12iz + 4z + 4z2 = 0

The solution to this equation could not be determined.

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