(2+6i)(8-7i)=0

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Solution for (2+6i)(8-7i)=0 equation: 


Simplifying
(2 + 6i)(8 + -7i) = 0

Multiply (2 + 6i) * (8 + -7i)
(2(8 + -7i) + 6i * (8 + -7i)) = 0
((8 * 2 + -7i * 2) + 6i * (8 + -7i)) = 0
((16 + -14i) + 6i * (8 + -7i)) = 0
(16 + -14i + (8 * 6i + -7i * 6i)) = 0
(16 + -14i + (48i + -42i2)) = 0

Combine like terms: -14i + 48i = 34i
(16 + 34i + -42i2) = 0

Solving
16 + 34i + -42i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 17i + -21i2) = 0

Factor a trinomial.
2((8 + -7i)(1 + 3i)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -7i)' equal to zero and attempt to solve:

Simplifying
8 + -7i = 0

Solving
8 + -7i = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7i = 0 + -8
-7i = 0 + -8

Combine like terms: 0 + -8 = -8
-7i = -8

Divide each side by '-7'.
i = 1.142857143

Simplifying
i = 1.142857143

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 = {1.142857143, -0.3333333333}

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