(2-3i)(4+6i+9i^2)=0

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Solution for (2-3i)(4+6i+9i^2)=0 equation:


Simplifying
(2 + -3i)(4 + 6i + 9i2) = 0

Multiply (2 + -3i) * (4 + 6i + 9i2)
(2(4 + 6i + 9i2) + -3i * (4 + 6i + 9i2)) = 0
((4 * 2 + 6i * 2 + 9i2 * 2) + -3i * (4 + 6i + 9i2)) = 0
((8 + 12i + 18i2) + -3i * (4 + 6i + 9i2)) = 0
(8 + 12i + 18i2 + (4 * -3i + 6i * -3i + 9i2 * -3i)) = 0
(8 + 12i + 18i2 + (-12i + -18i2 + -27i3)) = 0

Reorder the terms:
(8 + 12i + -12i + 18i2 + -18i2 + -27i3) = 0

Combine like terms: 12i + -12i = 0
(8 + 0 + 18i2 + -18i2 + -27i3) = 0
(8 + 18i2 + -18i2 + -27i3) = 0

Combine like terms: 18i2 + -18i2 = 0
(8 + 0 + -27i3) = 0
(8 + -27i3) = 0

Solving
8 + -27i3 = 0

Solving for variable 'i'.

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

Add '-8' to each side of the equation.
8 + -8 + -27i3 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -27i3 = 0 + -8
-27i3 = 0 + -8

Combine like terms: 0 + -8 = -8
-27i3 = -8

Divide each side by '-27'.
i3 = 0.2962962963

Simplifying
i3 = 0.2962962963

Reorder the terms:
-0.2962962963 + i3 = 0.2962962963 + -0.2962962963

Combine like terms: 0.2962962963 + -0.2962962963 = 0.0000000000
-0.2962962963 + i3 = 0.0000000000

The solution to this equation could not be determined.

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