(-1+2i)(6+i)=

Solution for (-1+2i)(6+i)= equation:

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

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

Combine like terms: -1i + 12i = 11i
(-6 + 11i + 2i2) = 0

Solving
-6 + 11i + 2i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-6 + -1i)(1 + -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 '(1 + -2i)' equal to zero and attempt to solve:

Simplifying
1 + -2i = 0

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

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

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

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5
Solution
i = {-6, 0.5}