3i(2+8i)(6+5i)=0

Solution for 3i(2+8i)(6+5i)=0 equation:

Simplifying
3i(2 + 8i)(6 + 5i) = 0

Multiply (2 + 8i) * (6 + 5i)
3i(2(6 + 5i) + 8i * (6 + 5i)) = 0
3i((6 * 2 + 5i * 2) + 8i * (6 + 5i)) = 0
3i((12 + 10i) + 8i * (6 + 5i)) = 0
3i(12 + 10i + (6 * 8i + 5i * 8i)) = 0
3i(12 + 10i + (48i + 40i2)) = 0

Combine like terms: 10i + 48i = 58i
3i(12 + 58i + 40i2) = 0
(12 * 3i + 58i * 3i + 40i2 * 3i) = 0
(36i + 174i2 + 120i3) = 0

Solving
36i + 174i2 + 120i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6i'.
6i(6 + 29i + 20i2) = 0

Factor a trinomial.
6i((6 + 5i)(1 + 4i)) = 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 '(6 + 5i)' equal to zero and attempt to solve:

Simplifying
6 + 5i = 0

Solving
6 + 5i = 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 + 5i = 0 + -6

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

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

Divide each side by '5'.
i = -1.2

Simplifying
i = -1.2
Subproblem 3
Set the factor '(1 + 4i)' equal to zero and attempt to solve:

Simplifying
1 + 4i = 0

Solving
1 + 4i = 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 + 4i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4i = 0 + -1
4i = 0 + -1

Combine like terms: 0 + -1 = -1
4i = -1

Divide each side by '4'.
i = -0.25

Simplifying
i = -0.25
Solution
i = {0, -1.2, -0.25}