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

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


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

Multiply (6 + -3i) * (8 + -3i)
i(6(8 + -3i) + -3i * (8 + -3i)) = 0
i((8 * 6 + -3i * 6) + -3i * (8 + -3i)) = 0
i((48 + -18i) + -3i * (8 + -3i)) = 0
i(48 + -18i + (8 * -3i + -3i * -3i)) = 0
i(48 + -18i + (-24i + 9i2)) = 0

Combine like terms: -18i + -24i = -42i
i(48 + -42i + 9i2) = 0
(48 * i + -42i * i + 9i2 * i) = 0
(48i + -42i2 + 9i3) = 0

Solving
48i + -42i2 + 9i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3i'.
3i(16 + -14i + 3i2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor 'i' equal to zero and attempt to solve:

Simplifying
i = 0

Solving
i = 0

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

Simplifying
i = 0

Subproblem 2
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 3
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 = {0, 2, 2.666666667}

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