(8-5i)(2+7i)=0

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Solution for (8-5i)(2+7i)=0 equation: 


Simplifying
(8 + -5i)(2 + 7i) = 0

Multiply (8 + -5i) * (2 + 7i)
(8(2 + 7i) + -5i * (2 + 7i)) = 0
((2 * 8 + 7i * 8) + -5i * (2 + 7i)) = 0
((16 + 56i) + -5i * (2 + 7i)) = 0
(16 + 56i + (2 * -5i + 7i * -5i)) = 0
(16 + 56i + (-10i + -35i2)) = 0

Combine like terms: 56i + -10i = 46i
(16 + 46i + -35i2) = 0

Solving
16 + 46i + -35i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(8 + -5i)(2 + 7i) = 0


Subproblem 1
Set the factor '(8 + -5i)' equal to zero and attempt to solve:

Simplifying
8 + -5i = 0

Solving
8 + -5i = 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 + -5i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5i = 0 + -8
-5i = 0 + -8

Combine like terms: 0 + -8 = -8
-5i = -8

Divide each side by '-5'.
i = 1.6

Simplifying
i = 1.6

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

Simplifying
2 + 7i = 0

Solving
2 + 7i = 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 + 7i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7i = 0 + -2
7i = 0 + -2

Combine like terms: 0 + -2 = -2
7i = -2

Divide each side by '7'.
i = -0.2857142857

Simplifying
i = -0.2857142857
Solution
i = {1.6, -0.2857142857}

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