(x+8i)(2x-9i)=

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Solution for (x+8i)(2x-9i)= equation: 


Simplifying
(x + 8i)(2x + -9i) = 0

Reorder the terms:
(8i + x)(2x + -9i) = 0

Reorder the terms:
(8i + x)(-9i + 2x) = 0

Multiply (8i + x) * (-9i + 2x)
(8i * (-9i + 2x) + x(-9i + 2x)) = 0
((-9i * 8i + 2x * 8i) + x(-9i + 2x)) = 0

Reorder the terms:
((16ix + -72i2) + x(-9i + 2x)) = 0
((16ix + -72i2) + x(-9i + 2x)) = 0
(16ix + -72i2 + (-9i * x + 2x * x)) = 0
(16ix + -72i2 + (-9ix + 2x2)) = 0

Reorder the terms:
(16ix + -9ix + -72i2 + 2x2) = 0

Combine like terms: 16ix + -9ix = 7ix
(7ix + -72i2 + 2x2) = 0

Solving
7ix + -72i2 + 2x2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-8i + -1x)(9i + -2x) = 0


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

Simplifying
-8i + -1x = 0

Solving
-8i + -1x = 0

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

Add 'x' to each side of the equation.
-8i + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-8i + 0 = 0 + x
-8i = 0 + x
Remove the zero:
-8i = x

Divide each side by '-8'.
i = -0.125x

Simplifying
i = -0.125x

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

Simplifying
9i + -2x = 0

Solving
9i + -2x = 0

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

Add '2x' to each side of the equation.
9i + -2x + 2x = 0 + 2x

Combine like terms: -2x + 2x = 0
9i + 0 = 0 + 2x
9i = 0 + 2x
Remove the zero:
9i = 2x

Divide each side by '9'.
i = 0.2222222222x

Simplifying
i = 0.2222222222x
Solution
i = {-0.125x, 0.2222222222x}

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