(6+2i)(8-3i)=

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Solution for (6+2i)(8-3i)= equation: 


Simplifying
(6 + 2i)(8 + -3i) = 0

Multiply (6 + 2i) * (8 + -3i)
(6(8 + -3i) + 2i * (8 + -3i)) = 0
((8 * 6 + -3i * 6) + 2i * (8 + -3i)) = 0
((48 + -18i) + 2i * (8 + -3i)) = 0
(48 + -18i + (8 * 2i + -3i * 2i)) = 0
(48 + -18i + (16i + -6i2)) = 0

Combine like terms: -18i + 16i = -2i
(48 + -2i + -6i2) = 0

Solving
48 + -2i + -6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + -1i + -3i2) = 0

Factor a trinomial.
2((8 + -3i)(3 + i)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -3i)' equal to zero and attempt to solve:

Simplifying
8 + -3i = 0

Solving
8 + -3i = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3i = 0 + -8
-3i = 0 + -8

Combine like terms: 0 + -8 = -8
-3i = -8

Divide each side by '-3'.
i = 2.666666667

Simplifying
i = 2.666666667

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

Simplifying
3 + i = 0

Solving
3 + i = 0

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

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

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

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

Simplifying
i = -3
Solution
i = {2.666666667, -3}

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