(16+6i)((12-10i)-(2-5i))=

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Solution for (16+6i)((12-10i)-(2-5i))= equation: 


Simplifying
(16 + 6i)((12 + -10i) + -1(2 + -5i)) = 0

Remove parenthesis around (12 + -10i)
(16 + 6i)(12 + -10i + -1(2 + -5i)) = 0
(16 + 6i)(12 + -10i + (2 * -1 + -5i * -1)) = 0
(16 + 6i)(12 + -10i + (-2 + 5i)) = 0

Reorder the terms:
(16 + 6i)(12 + -2 + -10i + 5i) = 0

Combine like terms: 12 + -2 = 10
(16 + 6i)(10 + -10i + 5i) = 0

Combine like terms: -10i + 5i = -5i
(16 + 6i)(10 + -5i) = 0

Multiply (16 + 6i) * (10 + -5i)
(16(10 + -5i) + 6i * (10 + -5i)) = 0
((10 * 16 + -5i * 16) + 6i * (10 + -5i)) = 0
((160 + -80i) + 6i * (10 + -5i)) = 0
(160 + -80i + (10 * 6i + -5i * 6i)) = 0
(160 + -80i + (60i + -30i2)) = 0

Combine like terms: -80i + 60i = -20i
(160 + -20i + -30i2) = 0

Solving
160 + -20i + -30i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '10'.
10(16 + -2i + -3i2) = 0

Factor a trinomial.
10((2 + -1i)(8 + 3i)) = 0

Ignore the factor 10.

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

Simplifying
2 + -1i = 0

Solving
2 + -1i = 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 + -1i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1i = 0 + -2
-1i = 0 + -2

Combine like terms: 0 + -2 = -2
-1i = -2

Divide each side by '-1'.
i = 2

Simplifying
i = 2

Subproblem 2
Set the factor '(8 + 3i)' equal to zero and attempt to solve:

Simplifying
8 + 3i = 0

Solving
8 + 3i = 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 + 3i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3i = 0 + -8
3i = 0 + -8

Combine like terms: 0 + -8 = -8
3i = -8

Divide each side by '3'.
i = -2.666666667

Simplifying
i = -2.666666667
Solution
i = {2, -2.666666667}

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