(-4i)(-5+4i)+(i)(-7-4i)=0

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Solution for (-4i)(-5+4i)+(i)(-7-4i)=0 equation: 


Simplifying
(-4i)(-5 + 4i) + (i)(-7 + -4i) = 0

Remove parenthesis around (-4i)
-4i(-5 + 4i) + (i)(-7 + -4i) = 0
(-5 * -4i + 4i * -4i) + (i)(-7 + -4i) = 0
(20i + -16i2) + (i)(-7 + -4i) = 0
20i + -16i2 + (-7 * i + -4i * i) = 0
20i + -16i2 + (-7i + -4i2) = 0

Reorder the terms:
20i + -7i + -16i2 + -4i2 = 0

Combine like terms: 20i + -7i = 13i
13i + -16i2 + -4i2 = 0

Combine like terms: -16i2 + -4i2 = -20i2
13i + -20i2 = 0

Solving
13i + -20i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), 'i'.
i(13 + -20i) = 0


Subproblem 1
Set the factor 'i' equal to zero and attempt to solve:

Simplifying
i = 0

Solving
i = 0

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

Simplifying
i = 0

Subproblem 2
Set the factor '(13 + -20i)' equal to zero and attempt to solve:

Simplifying
13 + -20i = 0

Solving
13 + -20i = 0

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

Add '-13' to each side of the equation.
13 + -13 + -20i = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -20i = 0 + -13
-20i = 0 + -13

Combine like terms: 0 + -13 = -13
-20i = -13

Divide each side by '-20'.
i = 0.65

Simplifying
i = 0.65
Solution
i = {0, 0.65}

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