(2-6i)(-4+6i)=0

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Solution for (2-6i)(-4+6i)=0 equation: 


Simplifying
(2 + -6i)(-4 + 6i) = 0

Multiply (2 + -6i) * (-4 + 6i)
(2(-4 + 6i) + -6i * (-4 + 6i)) = 0
((-4 * 2 + 6i * 2) + -6i * (-4 + 6i)) = 0
((-8 + 12i) + -6i * (-4 + 6i)) = 0
(-8 + 12i + (-4 * -6i + 6i * -6i)) = 0
(-8 + 12i + (24i + -36i2)) = 0

Combine like terms: 12i + 24i = 36i
(-8 + 36i + -36i2) = 0

Solving
-8 + 36i + -36i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + 9i + -9i2) = 0

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

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(1 + -3i)' equal to zero and attempt to solve:

Simplifying
1 + -3i = 0

Solving
1 + -3i = 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 + -3i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3i = 0 + -1
-3i = 0 + -1

Combine like terms: 0 + -1 = -1
-3i = -1

Divide each side by '-3'.
i = 0.3333333333

Simplifying
i = 0.3333333333
Solution
i = {0.6666666667, 0.3333333333}

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