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

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

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

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

Combine like terms: -10i + 6i = -4i
(12 + -4i + -5i2) = 0

Solving
12 + -4i + -5i2 = 0

Solving for variable 'i'.

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

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 + i)' equal to zero and attempt to solve:

Simplifying
2 + i = 0

Solving
2 + i = 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 + i = 0 + -2

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

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

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