=(8-3i)(-2-5i)

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Solution for =(8-3i)(-2-5i) equation: 


Simplifying
0 = (8 + -3i)(-2 + -5i)

Multiply (8 + -3i) * (-2 + -5i)
0 = (8(-2 + -5i) + -3i * (-2 + -5i))
0 = ((-2 * 8 + -5i * 8) + -3i * (-2 + -5i))
0 = ((-16 + -40i) + -3i * (-2 + -5i))
0 = (-16 + -40i + (-2 * -3i + -5i * -3i))
0 = (-16 + -40i + (6i + 15i2))

Combine like terms: -40i + 6i = -34i
0 = (-16 + -34i + 15i2)

Solving
0 = -16 + -34i + 15i2

Solving for variable 'i'.

Combine like terms: 0 + 16 = 16
16 + 34i + -15i2 = -16 + -34i + 15i2 + 16 + 34i + -15i2

Reorder the terms:
16 + 34i + -15i2 = -16 + 16 + -34i + 34i + 15i2 + -15i2

Combine like terms: -16 + 16 = 0
16 + 34i + -15i2 = 0 + -34i + 34i + 15i2 + -15i2
16 + 34i + -15i2 = -34i + 34i + 15i2 + -15i2

Combine like terms: -34i + 34i = 0
16 + 34i + -15i2 = 0 + 15i2 + -15i2
16 + 34i + -15i2 = 15i2 + -15i2

Combine like terms: 15i2 + -15i2 = 0
16 + 34i + -15i2 = 0

Factor a trinomial.
(8 + -3i)(2 + 5i) = 0


Subproblem 1
Set the factor '(8 + -3i)' equal to zero and attempt to solve:

Simplifying
8 + -3i = 0

Solving
8 + -3i = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3i = 0 + -8
-3i = 0 + -8

Combine like terms: 0 + -8 = -8
-3i = -8

Divide each side by '-3'.
i = 2.666666667

Simplifying
i = 2.666666667

Subproblem 2
Set the factor '(2 + 5i)' equal to zero and attempt to solve:

Simplifying
2 + 5i = 0

Solving
2 + 5i = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5i = 0 + -2
5i = 0 + -2

Combine like terms: 0 + -2 = -2
5i = -2

Divide each side by '5'.
i = -0.4

Simplifying
i = -0.4
Solution
i = {2.666666667, -0.4}

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