(4-3i)(2+6i)=0

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Solution for (4-3i)(2+6i)=0 equation: 


Simplifying
(4 + -3i)(2 + 6i) = 0

Multiply (4 + -3i) * (2 + 6i)
(4(2 + 6i) + -3i * (2 + 6i)) = 0
((2 * 4 + 6i * 4) + -3i * (2 + 6i)) = 0
((8 + 24i) + -3i * (2 + 6i)) = 0
(8 + 24i + (2 * -3i + 6i * -3i)) = 0
(8 + 24i + (-6i + -18i2)) = 0

Combine like terms: 24i + -6i = 18i
(8 + 18i + -18i2) = 0

Solving
8 + 18i + -18i2 = 0

Solving for variable 'i'.

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

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

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -3i)' equal to zero and attempt to solve:

Simplifying
4 + -3i = 0

Solving
4 + -3i = 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 + -3i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3i = 0 + -4
-3i = 0 + -4

Combine like terms: 0 + -4 = -4
-3i = -4

Divide each side by '-3'.
i = 1.333333333

Simplifying
i = 1.333333333

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 = {1.333333333, -0.3333333333}

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