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

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


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

Multiply (8 + i) * (6 + -3i)
(8(6 + -3i) + i(6 + -3i)) = 0
((6 * 8 + -3i * 8) + i(6 + -3i)) = 0
((48 + -24i) + i(6 + -3i)) = 0
(48 + -24i + (6 * i + -3i * i)) = 0
(48 + -24i + (6i + -3i2)) = 0

Combine like terms: -24i + 6i = -18i
(48 + -18i + -3i2) = 0

Solving
48 + -18i + -3i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(16 + -6i + -1i2) = 0

Factor a trinomial.
3((2 + -1i)(8 + i)) = 0

Ignore the factor 3.

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 '(8 + i)' equal to zero and attempt to solve:

Simplifying
8 + i = 0

Solving
8 + i = 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 + i = 0 + -8

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

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

Simplifying
i = -8
Solution
i = {2, -8}

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