=(-5+4i)(2+6i)

Solution for =(-5+4i)(2+6i) equation:

Simplifying
0 = (-5 + 4i)(2 + 6i)

Multiply (-5 + 4i) * (2 + 6i)
0 = (-5(2 + 6i) + 4i * (2 + 6i))
0 = ((2 * -5 + 6i * -5) + 4i * (2 + 6i))
0 = ((-10 + -30i) + 4i * (2 + 6i))
0 = (-10 + -30i + (2 * 4i + 6i * 4i))
0 = (-10 + -30i + (8i + 24i2))

Combine like terms: -30i + 8i = -22i
0 = (-10 + -22i + 24i2)

Solving
0 = -10 + -22i + 24i2

Solving for variable 'i'.

Combine like terms: 0 + 10 = 10
10 + 22i + -24i2 = -10 + -22i + 24i2 + 10 + 22i + -24i2

Reorder the terms:
10 + 22i + -24i2 = -10 + 10 + -22i + 22i + 24i2 + -24i2

Combine like terms: -10 + 10 = 0
10 + 22i + -24i2 = 0 + -22i + 22i + 24i2 + -24i2
10 + 22i + -24i2 = -22i + 22i + 24i2 + -24i2

Combine like terms: -22i + 22i = 0
10 + 22i + -24i2 = 0 + 24i2 + -24i2
10 + 22i + -24i2 = 24i2 + -24i2

Combine like terms: 24i2 + -24i2 = 0
10 + 22i + -24i2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 11i + -12i2) = 0

Factor a trinomial.
2((5 + -4i)(1 + 3i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -4i)' equal to zero and attempt to solve:

Simplifying
5 + -4i = 0

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

Combine like terms: 5 + -5 = 0
0 + -4i = 0 + -5
-4i = 0 + -5

Combine like terms: 0 + -5 = -5
-4i = -5

Divide each side by '-4'.
i = 1.25

Simplifying
i = 1.25
Subproblem 2
Set the factor '(1 + 3i)' equal to zero and attempt to solve:

Simplifying
1 + 3i = 0

Solving
1 + 3i = 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 + 3i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3i = 0 + -1
3i = 0 + -1

Combine like terms: 0 + -1 = -1
3i = -1

Divide each side by '3'.
i = -0.3333333333

Simplifying
i = -0.3333333333
Solution
i = {1.25, -0.3333333333}