(4-2i)(6-5i)=0

Solution for (4-2i)(6-5i)=0 equation:

Simplifying
(4 + -2i)(6 + -5i) = 0

Multiply (4 + -2i) * (6 + -5i)
(4(6 + -5i) + -2i * (6 + -5i)) = 0
((6 * 4 + -5i * 4) + -2i * (6 + -5i)) = 0
((24 + -20i) + -2i * (6 + -5i)) = 0
(24 + -20i + (6 * -2i + -5i * -2i)) = 0
(24 + -20i + (-12i + 10i2)) = 0

Combine like terms: -20i + -12i = -32i
(24 + -32i + 10i2) = 0

Solving
24 + -32i + 10i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -16i + 5i2) = 0

Factor a trinomial.
2((6 + -5i)(2 + -1i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -5i)' equal to zero and attempt to solve:

Simplifying
6 + -5i = 0

Solving
6 + -5i = 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 + -5i = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5i = 0 + -6
-5i = 0 + -6

Combine like terms: 0 + -6 = -6
-5i = -6

Divide each side by '-5'.
i = 1.2

Simplifying
i = 1.2
Subproblem 2
Set the factor '(2 + -1i)' equal to zero and attempt to solve:

Simplifying
2 + -1i = 0

Solving
2 + -1i = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1i = 0 + -2
-1i = 0 + -2

Combine like terms: 0 + -2 = -2
-1i = -2

Divide each side by '-1'.
i = 2

Simplifying
i = 2
Solution
i = {1.2, 2}