=(6+5i)(3-2i)

Solution for =(6+5i)(3-2i) equation:

Simplifying
0 = (6 + 5i)(3 + -2i)

Multiply (6 + 5i) * (3 + -2i)
0 = (6(3 + -2i) + 5i * (3 + -2i))
0 = ((3 * 6 + -2i * 6) + 5i * (3 + -2i))
0 = ((18 + -12i) + 5i * (3 + -2i))
0 = (18 + -12i + (3 * 5i + -2i * 5i))
0 = (18 + -12i + (15i + -10i2))

Combine like terms: -12i + 15i = 3i
0 = (18 + 3i + -10i2)

Solving
0 = 18 + 3i + -10i2

Solving for variable 'i'.

Combine like terms: 0 + -18 = -18
-18 + -3i + 10i2 = 18 + 3i + -10i2 + -18 + -3i + 10i2

Reorder the terms:
-18 + -3i + 10i2 = 18 + -18 + 3i + -3i + -10i2 + 10i2

Combine like terms: 18 + -18 = 0
-18 + -3i + 10i2 = 0 + 3i + -3i + -10i2 + 10i2
-18 + -3i + 10i2 = 3i + -3i + -10i2 + 10i2

Combine like terms: 3i + -3i = 0
-18 + -3i + 10i2 = 0 + -10i2 + 10i2
-18 + -3i + 10i2 = -10i2 + 10i2

Combine like terms: -10i2 + 10i2 = 0
-18 + -3i + 10i2 = 0

Factor a trinomial.
(-6 + -5i)(3 + -2i) = 0

Subproblem 1
Set the factor '(-6 + -5i)' equal to zero and attempt to solve:

Simplifying
-6 + -5i = 0

Solving
-6 + -5i = 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 + -5i = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5i = 0 + 6
-5i = 0 + 6

Combine like terms: 0 + 6 = 6
-5i = 6

Divide each side by '-5'.
i = -1.2

Simplifying
i = -1.2
Subproblem 2
Set the factor '(3 + -2i)' equal to zero and attempt to solve:

Simplifying
3 + -2i = 0

Solving
3 + -2i = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2i = 0 + -3
-2i = 0 + -3

Combine like terms: 0 + -3 = -3
-2i = -3

Divide each side by '-2'.
i = 1.5

Simplifying
i = 1.5
Solution
i = {-1.2, 1.5}