(8-i)x(7+2i)=

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


Simplifying
(8 + -1i) * x(7 + 2i) = 0

Reorder the terms for easier multiplication:
x(8 + -1i)(7 + 2i) = 0

Multiply (8 + -1i) * (7 + 2i)
x(8(7 + 2i) + -1i * (7 + 2i)) = 0
x((7 * 8 + 2i * 8) + -1i * (7 + 2i)) = 0
x((56 + 16i) + -1i * (7 + 2i)) = 0
x(56 + 16i + (7 * -1i + 2i * -1i)) = 0
x(56 + 16i + (-7i + -2i2)) = 0

Combine like terms: 16i + -7i = 9i
x(56 + 9i + -2i2) = 0
(56 * x + 9i * x + -2i2 * x) = 0

Reorder the terms:
(9ix + -2i2x + 56x) = 0
(9ix + -2i2x + 56x) = 0

Solving
9ix + -2i2x + 56x = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(9i + -2i2 + 56) = 0

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
-2i + -7 = 0

Reorder the terms:
-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

Subproblem 3
Set the factor '(i + -8)' equal to zero and attempt to solve:

Simplifying
i + -8 = 0

Reorder the terms:
-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
Solution
i = {-3.5, 8}

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