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

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


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

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

Combine like terms: -12i + 4i = -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 + -3i)(2 + i)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
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
Solution
i = {0.6666666667, -2}

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