(-6i)(-7-4i)+6(-6i)=0

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Solution for (-6i)(-7-4i)+6(-6i)=0 equation: 


Simplifying
(-6i)(-7 + -4i) + 6(-6i) = 0

Remove parenthesis around (-6i)
-6i(-7 + -4i) + 6(-6i) = 0
(-7 * -6i + -4i * -6i) + 6(-6i) = 0
(42i + 24i2) + 6(-6i) = 0

Remove parenthesis around (-6i)
42i + 24i2 + 6 * -6i = 0

Multiply 6 * -6
42i + 24i2 + -36i = 0

Reorder the terms:
42i + -36i + 24i2 = 0

Combine like terms: 42i + -36i = 6i
6i + 24i2 = 0

Solving
6i + 24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6i'.
6i(1 + 4i) = 0

Ignore the factor 6.

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 '(1 + 4i)' equal to zero and attempt to solve:

Simplifying
1 + 4i = 0

Solving
1 + 4i = 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 + 4i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4i = 0 + -1
4i = 0 + -1

Combine like terms: 0 + -1 = -1
4i = -1

Divide each side by '4'.
i = -0.25

Simplifying
i = -0.25
Solution
i = {0, -0.25}

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