=(3+2i)(4-3i)

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Solution for =(3+2i)(4-3i) equation: 


Simplifying
0 = (3 + 2i)(4 + -3i)

Multiply (3 + 2i) * (4 + -3i)
0 = (3(4 + -3i) + 2i * (4 + -3i))
0 = ((4 * 3 + -3i * 3) + 2i * (4 + -3i))
0 = ((12 + -9i) + 2i * (4 + -3i))
0 = (12 + -9i + (4 * 2i + -3i * 2i))
0 = (12 + -9i + (8i + -6i2))

Combine like terms: -9i + 8i = -1i
0 = (12 + -1i + -6i2)

Solving
0 = 12 + -1i + -6i2

Solving for variable 'i'.

Combine like terms: 0 + -12 = -12
-12 + i + 6i2 = 12 + -1i + -6i2 + -12 + i + 6i2

Reorder the terms:
-12 + i + 6i2 = 12 + -12 + -1i + i + -6i2 + 6i2

Combine like terms: 12 + -12 = 0
-12 + i + 6i2 = 0 + -1i + i + -6i2 + 6i2
-12 + i + 6i2 = -1i + i + -6i2 + 6i2

Combine like terms: -1i + i = 0
-12 + i + 6i2 = 0 + -6i2 + 6i2
-12 + i + 6i2 = -6i2 + 6i2

Combine like terms: -6i2 + 6i2 = 0
-12 + i + 6i2 = 0

Factor a trinomial.
(-3 + -2i)(4 + -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 '(4 + -3i)' equal to zero and attempt to solve:

Simplifying
4 + -3i = 0

Solving
4 + -3i = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3i = 0 + -4
-3i = 0 + -4

Combine like terms: 0 + -4 = -4
-3i = -4

Divide each side by '-3'.
i = 1.333333333

Simplifying
i = 1.333333333
Solution
i = {-1.5, 1.333333333}

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