(8+i)(5+3i)=0

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Solution for (8+i)(5+3i)=0 equation: 


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

Multiply (8 + i) * (5 + 3i)
(8(5 + 3i) + i(5 + 3i)) = 0
((5 * 8 + 3i * 8) + i(5 + 3i)) = 0
((40 + 24i) + i(5 + 3i)) = 0
(40 + 24i + (5 * i + 3i * i)) = 0
(40 + 24i + (5i + 3i2)) = 0

Combine like terms: 24i + 5i = 29i
(40 + 29i + 3i2) = 0

Solving
40 + 29i + 3i2 = 0

Solving for variable 'i'.

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


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

Simplifying
8 + i = 0

Solving
8 + i = 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 + i = 0 + -8

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

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

Simplifying
i = -8

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

Simplifying
5 + 3i = 0

Solving
5 + 3i = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3i = 0 + -5

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

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

Divide each side by '3'.
i = -1.666666667

Simplifying
i = -1.666666667
Solution
i = {-8, -1.666666667}

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