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

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


Simplifying
(7 + -1(6i))((-8) + (3i)) = 0

Remove parenthesis around (6i)
(7 + -1 * 6i)((-8) + (3i)) = 0

Multiply -1 * 6
(7 + -6i)((-8) + (3i)) = 0
(7 + -6i)(-8 + (3i)) = 0

Multiply (7 + -6i) * (-8 + (3i))
(7(-8 + (3i)) + -6i * (-8 + (3i))) = 0
((-8 * 7 + (3i) * 7) + -6i * (-8 + (3i))) = 0
((-56 + 21i) + -6i * (-8 + (3i))) = 0
(-56 + 21i + (-8 * -6i + (3i) * -6i)) = 0
(-56 + 21i + (48i + -18i2)) = 0

Combine like terms: 21i + 48i = 69i
(-56 + 69i + -18i2) = 0

Solving
-56 + 69i + -18i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-8 + 3i)(7 + -6i) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -6i)' equal to zero and attempt to solve:

Simplifying
7 + -6i = 0

Solving
7 + -6i = 0

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

Add '-7' to each side of the equation.
7 + -7 + -6i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6i = 0 + -7
-6i = 0 + -7

Combine like terms: 0 + -7 = -7
-6i = -7

Divide each side by '-6'.
i = 1.166666667

Simplifying
i = 1.166666667
Solution
i = {2.666666667, 1.166666667}

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