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

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


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

Reorder the terms:
(8 + 3i)(6i + -7) = 0

Reorder the terms:
(8 + 3i)(-7 + 6i) = 0

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

Combine like terms: 48i + -21i = 27i
(-56 + 27i + 18i2) = 0

Solving
-56 + 27i + 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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