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

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


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

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

Combine like terms: -35i + -16i = -51i
(56 + -51i + 10i2) = 0

Solving
56 + -51i + 10i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(8 + -5i)(7 + -2i) = 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 '(7 + -2i)' equal to zero and attempt to solve:

Simplifying
7 + -2i = 0

Solving
7 + -2i = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2i = 0 + -7

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

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

Divide each side by '-2'.
i = 3.5

Simplifying
i = 3.5
Solution
i = {1.6, 3.5}

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