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

Solution for (4-i)(6+i)=0 equation:

Simplifying
(4 + -1i)(6 + i) = 0

Multiply (4 + -1i) * (6 + i)
(4(6 + i) + -1i * (6 + i)) = 0
((6 * 4 + i * 4) + -1i * (6 + i)) = 0
((24 + 4i) + -1i * (6 + i)) = 0
(24 + 4i + (6 * -1i + i * -1i)) = 0
(24 + 4i + (-6i + -1i2)) = 0

Combine like terms: 4i + -6i = -2i
(24 + -2i + -1i2) = 0

Solving
24 + -2i + -1i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(4 + -1i)(6 + i) = 0

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

Simplifying
4 + -1i = 0

Solving
4 + -1i = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1i = 0 + -4

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

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

Divide each side by '-1'.
i = 4

Simplifying
i = 4
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 = {4, -6}