(2-i)(3i-2)=0

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Solution for (2-i)(3i-2)=0 equation: 


Simplifying
(2 + -1i)(3i + -2) = 0

Reorder the terms:
(2 + -1i)(-2 + 3i) = 0

Multiply (2 + -1i) * (-2 + 3i)
(2(-2 + 3i) + -1i * (-2 + 3i)) = 0
((-2 * 2 + 3i * 2) + -1i * (-2 + 3i)) = 0
((-4 + 6i) + -1i * (-2 + 3i)) = 0
(-4 + 6i + (-2 * -1i + 3i * -1i)) = 0
(-4 + 6i + (2i + -3i2)) = 0

Combine like terms: 6i + 2i = 8i
(-4 + 8i + -3i2) = 0

Solving
-4 + 8i + -3i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-2 + i)(2 + -3i) = 0


Subproblem 1
Set the factor '(-2 + i)' equal to zero and attempt to solve:

Simplifying
-2 + i = 0

Solving
-2 + i = 0

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

Add '2' to each side of the equation.
-2 + 2 + i = 0 + 2

Combine like terms: -2 + 2 = 0
0 + i = 0 + 2
i = 0 + 2

Combine like terms: 0 + 2 = 2
i = 2

Simplifying
i = 2

Subproblem 2
Set the factor '(2 + -3i)' equal to zero and attempt to solve:

Simplifying
2 + -3i = 0

Solving
2 + -3i = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3i = 0 + -2
-3i = 0 + -2

Combine like terms: 0 + -2 = -2
-3i = -2

Divide each side by '-3'.
i = 0.6666666667

Simplifying
i = 0.6666666667
Solution
i = {2, 0.6666666667}

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