(1-6i)(3+i)=0

Solution for (1-6i)(3+i)=0 equation:

Simplifying
(1 + -6i)(3 + i) = 0

Multiply (1 + -6i) * (3 + i)
(1(3 + i) + -6i * (3 + i)) = 0
((3 * 1 + i * 1) + -6i * (3 + i)) = 0
((3 + 1i) + -6i * (3 + i)) = 0
(3 + 1i + (3 * -6i + i * -6i)) = 0
(3 + 1i + (-18i + -6i2)) = 0

Combine like terms: 1i + -18i = -17i
(3 + -17i + -6i2) = 0

Solving
3 + -17i + -6i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(1 + -6i)(3 + i) = 0

Subproblem 1
Set the factor '(1 + -6i)' equal to zero and attempt to solve:

Simplifying
1 + -6i = 0

Solving
1 + -6i = 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 + -6i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6i = 0 + -1
-6i = 0 + -1

Combine like terms: 0 + -1 = -1
-6i = -1

Divide each side by '-6'.
i = 0.1666666667

Simplifying
i = 0.1666666667
Subproblem 2
Set the factor '(3 + i)' equal to zero and attempt to solve:

Simplifying
3 + i = 0

Solving
3 + i = 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 + i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + i = 0 + -3
i = 0 + -3

Combine like terms: 0 + -3 = -3
i = -3

Simplifying
i = -3
Solution
i = {0.1666666667, -3}