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

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Solution for (-6-3i)(8-i)=0 equation: 


Simplifying
(-6 + -3i)(8 + -1i) = 0

Multiply (-6 + -3i) * (8 + -1i)
(-6(8 + -1i) + -3i * (8 + -1i)) = 0
((8 * -6 + -1i * -6) + -3i * (8 + -1i)) = 0
((-48 + 6i) + -3i * (8 + -1i)) = 0
(-48 + 6i + (8 * -3i + -1i * -3i)) = 0
(-48 + 6i + (-24i + 3i2)) = 0

Combine like terms: 6i + -24i = -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 + i2) = 0

Factor a trinomial.
3((-2 + -1i)(8 + -1i)) = 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 + -1i)' equal to zero and attempt to solve:

Simplifying
8 + -1i = 0

Solving
8 + -1i = 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 + -1i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1i = 0 + -8
-1i = 0 + -8

Combine like terms: 0 + -8 = -8
-1i = -8

Divide each side by '-1'.
i = 8

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

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