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


Subproblem 1
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

Subproblem 2
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
Solution
i = {0.2857142857, -1.6}

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