(5+i)x(1-4i)=0

Solution for (5+i)x(1-4i)=0 equation:

Simplifying
(5 + i) * x(1 + -4i) = 0

Reorder the terms for easier multiplication:
x(5 + i)(1 + -4i) = 0

Multiply (5 + i) * (1 + -4i)
x(5(1 + -4i) + i(1 + -4i)) = 0
x((1 * 5 + -4i * 5) + i(1 + -4i)) = 0
x((5 + -20i) + i(1 + -4i)) = 0
x(5 + -20i + (1 * i + -4i * i)) = 0
x(5 + -20i + (1i + -4i2)) = 0

Combine like terms: -20i + 1i = -19i
x(5 + -19i + -4i2) = 0
(5 * x + -19i * x + -4i2 * x) = 0

Reorder the terms:
(-19ix + -4i2x + 5x) = 0
(-19ix + -4i2x + 5x) = 0

Solving
-19ix + -4i2x + 5x = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-19i + -4i2 + 5) = 0

Factor a trinomial.
x((-1i + -5)(4i + -1)) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-1i + -5)' equal to zero and attempt to solve:

Simplifying
-1i + -5 = 0

Reorder the terms:
-5 + -1i = 0

Solving
-5 + -1i = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1i = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1i = 0 + 5
-1i = 0 + 5

Combine like terms: 0 + 5 = 5
-1i = 5

Divide each side by '-1'.
i = -5

Simplifying
i = -5
Subproblem 3
Set the factor '(4i + -1)' equal to zero and attempt to solve:

Simplifying
4i + -1 = 0

Reorder the terms:
-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 = {-5, 0.25}