3i(4-2i)(5+6i)=

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Solution for 3i(4-2i)(5+6i)= equation: 


Simplifying
3i(4 + -2i)(5 + 6i) = 0

Multiply (4 + -2i) * (5 + 6i)
3i(4(5 + 6i) + -2i * (5 + 6i)) = 0
3i((5 * 4 + 6i * 4) + -2i * (5 + 6i)) = 0
3i((20 + 24i) + -2i * (5 + 6i)) = 0
3i(20 + 24i + (5 * -2i + 6i * -2i)) = 0
3i(20 + 24i + (-10i + -12i2)) = 0

Combine like terms: 24i + -10i = 14i
3i(20 + 14i + -12i2) = 0
(20 * 3i + 14i * 3i + -12i2 * 3i) = 0
(60i + 42i2 + -36i3) = 0

Solving
60i + 42i2 + -36i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6i'.
6i(10 + 7i + -6i2) = 0

Factor a trinomial.
6i((2 + -1i)(5 + 6i)) = 0

Ignore the factor 6.

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 '(5 + 6i)' equal to zero and attempt to solve:

Simplifying
5 + 6i = 0

Solving
5 + 6i = 0

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

Add '-5' to each side of the equation.
5 + -5 + 6i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6i = 0 + -5
6i = 0 + -5

Combine like terms: 0 + -5 = -5
6i = -5

Divide each side by '6'.
i = -0.8333333333

Simplifying
i = -0.8333333333
Solution
i = {0, 2, -0.8333333333}

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