-2i(1+i)(2+3i)=

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Solution for -2i(1+i)(2+3i)= equation: 


Simplifying
-2i(1 + i)(2 + 3i) = 0

Multiply (1 + i) * (2 + 3i)
-2i(1(2 + 3i) + i(2 + 3i)) = 0
-2i((2 * 1 + 3i * 1) + i(2 + 3i)) = 0
-2i((2 + 3i) + i(2 + 3i)) = 0
-2i(2 + 3i + (2 * i + 3i * i)) = 0
-2i(2 + 3i + (2i + 3i2)) = 0

Combine like terms: 3i + 2i = 5i
-2i(2 + 5i + 3i2) = 0
(2 * -2i + 5i * -2i + 3i2 * -2i) = 0
(-4i + -10i2 + -6i3) = 0

Solving
-4i + -10i2 + -6i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-2i'.
-2i(2 + 5i + 3i2) = 0

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

Ignore the factor -2.

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

Simplifying
1 + i = 0

Solving
1 + i = 0

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

Add '-1' to each side of the equation.
1 + -1 + i = 0 + -1

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

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

Simplifying
i = -1

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, -1, -0.6666666667}

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