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

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


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

Multiply (3 + 2i) * (7 + -3i)
0 = (3(7 + -3i) + 2i * (7 + -3i))
0 = ((7 * 3 + -3i * 3) + 2i * (7 + -3i))
0 = ((21 + -9i) + 2i * (7 + -3i))
0 = (21 + -9i + (7 * 2i + -3i * 2i))
0 = (21 + -9i + (14i + -6i2))

Combine like terms: -9i + 14i = 5i
0 = (21 + 5i + -6i2)

Solving
0 = 21 + 5i + -6i2

Solving for variable 'i'.

Combine like terms: 0 + -21 = -21
-21 + -5i + 6i2 = 21 + 5i + -6i2 + -21 + -5i + 6i2

Reorder the terms:
-21 + -5i + 6i2 = 21 + -21 + 5i + -5i + -6i2 + 6i2

Combine like terms: 21 + -21 = 0
-21 + -5i + 6i2 = 0 + 5i + -5i + -6i2 + 6i2
-21 + -5i + 6i2 = 5i + -5i + -6i2 + 6i2

Combine like terms: 5i + -5i = 0
-21 + -5i + 6i2 = 0 + -6i2 + 6i2
-21 + -5i + 6i2 = -6i2 + 6i2

Combine like terms: -6i2 + 6i2 = 0
-21 + -5i + 6i2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -3i)' equal to zero and attempt to solve:

Simplifying
7 + -3i = 0

Solving
7 + -3i = 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 + -3i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3i = 0 + -7
-3i = 0 + -7

Combine like terms: 0 + -7 = -7
-3i = -7

Divide each side by '-3'.
i = 2.333333333

Simplifying
i = 2.333333333
Solution
i = {-1.5, 2.333333333}

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