(-8-9i)(5+i)=0

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Solution for (-8-9i)(5+i)=0 equation: 


Simplifying
(-8 + -9i)(5 + i) = 0

Multiply (-8 + -9i) * (5 + i)
(-8(5 + i) + -9i * (5 + i)) = 0
((5 * -8 + i * -8) + -9i * (5 + i)) = 0
((-40 + -8i) + -9i * (5 + i)) = 0
(-40 + -8i + (5 * -9i + i * -9i)) = 0
(-40 + -8i + (-45i + -9i2)) = 0

Combine like terms: -8i + -45i = -53i
(-40 + -53i + -9i2) = 0

Solving
-40 + -53i + -9i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(40 + 53i + 9i2) = 0

Factor a trinomial.
-1((5 + i)(8 + 9i)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + i)' equal to zero and attempt to solve:

Simplifying
5 + i = 0

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

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

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

Simplifying
i = -5

Subproblem 2
Set the factor '(8 + 9i)' equal to zero and attempt to solve:

Simplifying
8 + 9i = 0

Solving
8 + 9i = 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 + 9i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 9i = 0 + -8
9i = 0 + -8

Combine like terms: 0 + -8 = -8
9i = -8

Divide each side by '9'.
i = -0.8888888889

Simplifying
i = -0.8888888889
Solution
i = {-5, -0.8888888889}

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