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

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

Simplifying
(5 + 2i)(6 + -1i) = 0

Multiply (5 + 2i) * (6 + -1i)
(5(6 + -1i) + 2i * (6 + -1i)) = 0
((6 * 5 + -1i * 5) + 2i * (6 + -1i)) = 0
((30 + -5i) + 2i * (6 + -1i)) = 0
(30 + -5i + (6 * 2i + -1i * 2i)) = 0
(30 + -5i + (12i + -2i2)) = 0

Combine like terms: -5i + 12i = 7i
(30 + 7i + -2i2) = 0

Solving
30 + 7i + -2i2 = 0

Solving for variable 'i'.

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

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

Simplifying
6 + -1i = 0

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

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

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

Divide each side by '-1'.
i = 6

Simplifying
i = 6
Subproblem 2
Set the factor '(5 + 2i)' equal to zero and attempt to solve:

Simplifying
5 + 2i = 0

Solving
5 + 2i = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2i = 0 + -5
2i = 0 + -5

Combine like terms: 0 + -5 = -5
2i = -5

Divide each side by '2'.
i = -2.5

Simplifying
i = -2.5
Solution
i = {6, -2.5}