=(7+2i)(3-5i)

Solution for =(7+2i)(3-5i) equation:

Simplifying
0 = (7 + 2i)(3 + -5i)

Multiply (7 + 2i) * (3 + -5i)
0 = (7(3 + -5i) + 2i * (3 + -5i))
0 = ((3 * 7 + -5i * 7) + 2i * (3 + -5i))
0 = ((21 + -35i) + 2i * (3 + -5i))
0 = (21 + -35i + (3 * 2i + -5i * 2i))
0 = (21 + -35i + (6i + -10i2))

Combine like terms: -35i + 6i = -29i
0 = (21 + -29i + -10i2)

Solving
0 = 21 + -29i + -10i2

Solving for variable 'i'.

Combine like terms: 0 + -21 = -21
-21 + 29i + 10i2 = 21 + -29i + -10i2 + -21 + 29i + 10i2

Reorder the terms:
-21 + 29i + 10i2 = 21 + -21 + -29i + 29i + -10i2 + 10i2

Combine like terms: 21 + -21 = 0
-21 + 29i + 10i2 = 0 + -29i + 29i + -10i2 + 10i2
-21 + 29i + 10i2 = -29i + 29i + -10i2 + 10i2

Combine like terms: -29i + 29i = 0
-21 + 29i + 10i2 = 0 + -10i2 + 10i2
-21 + 29i + 10i2 = -10i2 + 10i2

Combine like terms: -10i2 + 10i2 = 0
-21 + 29i + 10i2 = 0

Factor a trinomial.
(-7 + -2i)(3 + -5i) = 0

Subproblem 1
Set the factor '(-7 + -2i)' equal to zero and attempt to solve:

Simplifying
-7 + -2i = 0

Solving
-7 + -2i = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2i = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2i = 0 + 7
-2i = 0 + 7

Combine like terms: 0 + 7 = 7
-2i = 7

Divide each side by '-2'.
i = -3.5

Simplifying
i = -3.5
Subproblem 2
Set the factor '(3 + -5i)' equal to zero and attempt to solve:

Simplifying
3 + -5i = 0

Solving
3 + -5i = 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 + -5i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5i = 0 + -3
-5i = 0 + -3

Combine like terms: 0 + -3 = -3
-5i = -3

Divide each side by '-5'.
i = 0.6

Simplifying
i = 0.6
Solution
i = {-3.5, 0.6}