i(8+3i)(8+3i)=0

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Solution for i(8+3i)(8+3i)=0 equation: 


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

Multiply (8 + 3i) * (8 + 3i)
i(8(8 + 3i) + 3i * (8 + 3i)) = 0
i((8 * 8 + 3i * 8) + 3i * (8 + 3i)) = 0
i((64 + 24i) + 3i * (8 + 3i)) = 0
i(64 + 24i + (8 * 3i + 3i * 3i)) = 0
i(64 + 24i + (24i + 9i2)) = 0

Combine like terms: 24i + 24i = 48i
i(64 + 48i + 9i2) = 0
(64 * i + 48i * i + 9i2 * i) = 0
(64i + 48i2 + 9i3) = 0

Solving
64i + 48i2 + 9i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), 'i'.
i(64 + 48i + 9i2) = 0

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


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 '(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 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, -2.666666667, -2.666666667}

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