(3-7i)(8+6i)=0

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Solution for (3-7i)(8+6i)=0 equation: 


Simplifying
(3 + -7i)(8 + 6i) = 0

Multiply (3 + -7i) * (8 + 6i)
(3(8 + 6i) + -7i * (8 + 6i)) = 0
((8 * 3 + 6i * 3) + -7i * (8 + 6i)) = 0
((24 + 18i) + -7i * (8 + 6i)) = 0
(24 + 18i + (8 * -7i + 6i * -7i)) = 0
(24 + 18i + (-56i + -42i2)) = 0

Combine like terms: 18i + -56i = -38i
(24 + -38i + -42i2) = 0

Solving
24 + -38i + -42i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -19i + -21i2) = 0

Factor a trinomial.
2((3 + -7i)(4 + 3i)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -7i)' equal to zero and attempt to solve:

Simplifying
3 + -7i = 0

Solving
3 + -7i = 0

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

Add '-3' to each side of the equation.
3 + -3 + -7i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7i = 0 + -3
-7i = 0 + -3

Combine like terms: 0 + -3 = -3
-7i = -3

Divide each side by '-7'.
i = 0.4285714286

Simplifying
i = 0.4285714286

Subproblem 2
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
Solution
i = {0.4285714286, -1.333333333}

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