i(6+4i)(6-4i)=

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

Simplifying
i(6 + 4i)(6 + -4i) = 0

Multiply (6 + 4i) * (6 + -4i)
i(6(6 + -4i) + 4i * (6 + -4i)) = 0
i((6 * 6 + -4i * 6) + 4i * (6 + -4i)) = 0
i((36 + -24i) + 4i * (6 + -4i)) = 0
i(36 + -24i + (6 * 4i + -4i * 4i)) = 0
i(36 + -24i + (24i + -16i2)) = 0

Combine like terms: -24i + 24i = 0
i(36 + 0 + -16i2) = 0
i(36 + -16i2) = 0
(36 * i + -16i2 * i) = 0
(36i + -16i3) = 0

Solving
36i + -16i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4i'.
4i(9 + -4i2) = 0

Factor a difference between two squares.
4i((3 + 2i)(3 + -2i)) = 0

Ignore the factor 4.
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 '(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, -1.5, 1.5}