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

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Solution for (-4-4i)(2-3i)=0 equation: 


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

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

Combine like terms: 12i + -8i = 4i
(-8 + 4i + 12i2) = 0

Solving
-8 + 4i + 12i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + i + 3i2) = 0

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

Ignore the factor 4.

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

Simplifying
-1 + -1i = 0

Solving
-1 + -1i = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1i = 0 + 1

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

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

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

Simplifying
i = -1

Subproblem 2
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
Solution
i = {-1, 0.6666666667}

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