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

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


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

Remove parenthesis around (6i)
6i(5 + i)(-2 + 3i) = 0

Multiply (5 + i) * (-2 + 3i)
6i(5(-2 + 3i) + i(-2 + 3i)) = 0
6i((-2 * 5 + 3i * 5) + i(-2 + 3i)) = 0
6i((-10 + 15i) + i(-2 + 3i)) = 0
6i(-10 + 15i + (-2 * i + 3i * i)) = 0
6i(-10 + 15i + (-2i + 3i2)) = 0

Combine like terms: 15i + -2i = 13i
6i(-10 + 13i + 3i2) = 0
(-10 * 6i + 13i * 6i + 3i2 * 6i) = 0
(-60i + 78i2 + 18i3) = 0

Solving
-60i + 78i2 + 18i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6i'.
6i(-10 + 13i + 3i2) = 0

Factor a trinomial.
6i((-5 + -1i)(2 + -3i)) = 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 '(-5 + -1i)' equal to zero and attempt to solve:

Simplifying
-5 + -1i = 0

Solving
-5 + -1i = 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 + -1i = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1i = 0 + 5
-1i = 0 + 5

Combine like terms: 0 + 5 = 5
-1i = 5

Divide each side by '-1'.
i = -5

Simplifying
i = -5

Subproblem 3
Set the factor '(2 + -3i)' equal to zero and attempt to solve:

Simplifying
2 + -3i = 0

Solving
2 + -3i = 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 + -3i = 0 + -2

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

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

Divide each side by '-3'.
i = 0.6666666667

Simplifying
i = 0.6666666667
Solution
i = {0, -5, 0.6666666667}

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