5i(8i-2)=0

Solution for 5i(8i-2)=0 equation:

Simplifying
5i(8i + -2) = 0

Reorder the terms:
5i(-2 + 8i) = 0
(-2 * 5i + 8i * 5i) = 0
(-10i + 40i2) = 0

Solving
-10i + 40i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '10i'.
10i(-1 + 4i) = 0

Ignore the factor 10.
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 + 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, 0.25}