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

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

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

Multiply (-6 + -1i) * (-1 + 6i)
(-6(-1 + 6i) + -1i * (-1 + 6i)) = 0
((-1 * -6 + 6i * -6) + -1i * (-1 + 6i)) = 0
((6 + -36i) + -1i * (-1 + 6i)) = 0
(6 + -36i + (-1 * -1i + 6i * -1i)) = 0
(6 + -36i + (1i + -6i2)) = 0

Combine like terms: -36i + 1i = -35i
(6 + -35i + -6i2) = 0

Solving
6 + -35i + -6i2 = 0

Solving for variable 'i'.

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

Simplifying
6 + i = 0

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

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

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

Simplifying
i = -6
Solution
i = {0.1666666667, -6}