5i(3+2i)(8+3i)=0

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Solution for 5i(3+2i)(8+3i)=0 equation: 


Simplifying
5i(3 + 2i)(8 + 3i) = 0

Multiply (3 + 2i) * (8 + 3i)
5i(3(8 + 3i) + 2i * (8 + 3i)) = 0
5i((8 * 3 + 3i * 3) + 2i * (8 + 3i)) = 0
5i((24 + 9i) + 2i * (8 + 3i)) = 0
5i(24 + 9i + (8 * 2i + 3i * 2i)) = 0
5i(24 + 9i + (16i + 6i2)) = 0

Combine like terms: 9i + 16i = 25i
5i(24 + 25i + 6i2) = 0
(24 * 5i + 25i * 5i + 6i2 * 5i) = 0
(120i + 125i2 + 30i3) = 0

Solving
120i + 125i2 + 30i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '5i'.
5i(24 + 25i + 6i2) = 0

Factor a trinomial.
5i((8 + 3i)(3 + 2i)) = 0

Ignore the factor 5.

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 '(3 + 2i)' equal to zero and attempt to solve:

Simplifying
3 + 2i = 0

Solving
3 + 2i = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2i = 0 + -3
2i = 0 + -3

Combine like terms: 0 + -3 = -3
2i = -3

Divide each side by '2'.
i = -1.5

Simplifying
i = -1.5
Solution
i = {0, -2.666666667, -1.5}

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