(3i+2)(4-2i)=

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Solution for (3i+2)(4-2i)= equation: 


Simplifying
(3i + 2)(4 + -2i) = 0

Reorder the terms:
(2 + 3i)(4 + -2i) = 0

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

Combine like terms: -4i + 12i = 8i
(8 + 8i + -6i2) = 0

Solving
8 + 8i + -6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 4i + -3i2) = 0

Factor a trinomial.
2((2 + -1i)(2 + 3i)) = 0

Ignore the factor 2.

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

Simplifying
2 + -1i = 0

Solving
2 + -1i = 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 + -1i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1i = 0 + -2
-1i = 0 + -2

Combine like terms: 0 + -2 = -2
-1i = -2

Divide each side by '-1'.
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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