=(4+2i)(-1+5i)

Solution for =(4+2i)(-1+5i) equation:

Simplifying
0 = (4 + 2i)(-1 + 5i)

Multiply (4 + 2i) * (-1 + 5i)
0 = (4(-1 + 5i) + 2i * (-1 + 5i))
0 = ((-1 * 4 + 5i * 4) + 2i * (-1 + 5i))
0 = ((-4 + 20i) + 2i * (-1 + 5i))
0 = (-4 + 20i + (-1 * 2i + 5i * 2i))
0 = (-4 + 20i + (-2i + 10i2))

Combine like terms: 20i + -2i = 18i
0 = (-4 + 18i + 10i2)

Solving
0 = -4 + 18i + 10i2

Solving for variable 'i'.

Combine like terms: 0 + 4 = 4
4 + -18i + -10i2 = -4 + 18i + 10i2 + 4 + -18i + -10i2

Reorder the terms:
4 + -18i + -10i2 = -4 + 4 + 18i + -18i + 10i2 + -10i2

Combine like terms: -4 + 4 = 0
4 + -18i + -10i2 = 0 + 18i + -18i + 10i2 + -10i2
4 + -18i + -10i2 = 18i + -18i + 10i2 + -10i2

Combine like terms: 18i + -18i = 0
4 + -18i + -10i2 = 0 + 10i2 + -10i2
4 + -18i + -10i2 = 10i2 + -10i2

Combine like terms: 10i2 + -10i2 = 0
4 + -18i + -10i2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -9i + -5i2) = 0

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

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

Simplifying
1 + -5i = 0

Solving
1 + -5i = 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 + -5i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5i = 0 + -1
-5i = 0 + -1

Combine like terms: 0 + -1 = -1
-5i = -1

Divide each side by '-5'.
i = 0.2

Simplifying
i = 0.2
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 = {0.2, -2}