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

Solution for =(1+6i)(5-2i) equation:

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

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

Combine like terms: -2i + 30i = 28i
0 = (5 + 28i + -12i2)

Solving
0 = 5 + 28i + -12i2

Solving for variable 'i'.

Combine like terms: 0 + -5 = -5
-5 + -28i + 12i2 = 5 + 28i + -12i2 + -5 + -28i + 12i2

Reorder the terms:
-5 + -28i + 12i2 = 5 + -5 + 28i + -28i + -12i2 + 12i2

Combine like terms: 5 + -5 = 0
-5 + -28i + 12i2 = 0 + 28i + -28i + -12i2 + 12i2
-5 + -28i + 12i2 = 28i + -28i + -12i2 + 12i2

Combine like terms: 28i + -28i = 0
-5 + -28i + 12i2 = 0 + -12i2 + 12i2
-5 + -28i + 12i2 = -12i2 + 12i2

Combine like terms: -12i2 + 12i2 = 0
-5 + -28i + 12i2 = 0

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

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

Simplifying
-1 + -6i = 0

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

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

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

Divide each side by '-6'.
i = -0.1666666667

Simplifying
i = -0.1666666667
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 = {-0.1666666667, 2.5}