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

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

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

Multiply (6 + i) * (3 + -2i)
i(6(3 + -2i) + i(3 + -2i)) = 0
i((3 * 6 + -2i * 6) + i(3 + -2i)) = 0
i((18 + -12i) + i(3 + -2i)) = 0
i(18 + -12i + (3 * i + -2i * i)) = 0
i(18 + -12i + (3i + -2i2)) = 0

Combine like terms: -12i + 3i = -9i
i(18 + -9i + -2i2) = 0
(18 * i + -9i * i + -2i2 * i) = 0
(18i + -9i2 + -2i3) = 0

Solving
18i + -9i2 + -2i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), 'i'.
i(18 + -9i + -2i2) = 0

Factor a trinomial.
i((3 + -2i)(6 + i)) = 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 '(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
Subproblem 3
Set the factor '(6 + i)' equal to zero and attempt to solve:

Simplifying
6 + i = 0

Solving
6 + i = 0

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

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

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

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

Simplifying
i = -6
Solution
i = {0, 1.5, -6}