(6-3i)(-4-5i)=0

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Solution for (6-3i)(-4-5i)=0 equation: 


Simplifying
(6 + -3i)(-4 + -5i) = 0

Multiply (6 + -3i) * (-4 + -5i)
(6(-4 + -5i) + -3i * (-4 + -5i)) = 0
((-4 * 6 + -5i * 6) + -3i * (-4 + -5i)) = 0
((-24 + -30i) + -3i * (-4 + -5i)) = 0
(-24 + -30i + (-4 * -3i + -5i * -3i)) = 0
(-24 + -30i + (12i + 15i2)) = 0

Combine like terms: -30i + 12i = -18i
(-24 + -18i + 15i2) = 0

Solving
-24 + -18i + 15i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -6i + 5i2) = 0

Factor a trinomial.
3((-4 + -5i)(2 + -1i)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -5i)' equal to zero and attempt to solve:

Simplifying
-4 + -5i = 0

Solving
-4 + -5i = 0

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

Add '4' to each side of the equation.
-4 + 4 + -5i = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5i = 0 + 4
-5i = 0 + 4

Combine like terms: 0 + 4 = 4
-5i = 4

Divide each side by '-5'.
i = -0.8

Simplifying
i = -0.8

Subproblem 2
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
Solution
i = {-0.8, 2}

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