(8+i)x(-4-3i)=

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Solution for (8+i)x(-4-3i)= equation: 


Simplifying
(8 + i) * x(-4 + -3i) = 0

Reorder the terms for easier multiplication:
x(8 + i)(-4 + -3i) = 0

Multiply (8 + i) * (-4 + -3i)
x(8(-4 + -3i) + i(-4 + -3i)) = 0
x((-4 * 8 + -3i * 8) + i(-4 + -3i)) = 0
x((-32 + -24i) + i(-4 + -3i)) = 0
x(-32 + -24i + (-4 * i + -3i * i)) = 0
x(-32 + -24i + (-4i + -3i2)) = 0

Combine like terms: -24i + -4i = -28i
x(-32 + -28i + -3i2) = 0
(-32 * x + -28i * x + -3i2 * x) = 0

Reorder the terms:
(-28ix + -3i2x + -32x) = 0
(-28ix + -3i2x + -32x) = 0

Solving
-28ix + -3i2x + -32x = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(28i + 3i2 + 32) = 0

Factor a trinomial.
-1x((3i + 4)(i + 8)) = 0

Ignore the factor -1.

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 '(3i + 4)' equal to zero and attempt to solve:

Simplifying
3i + 4 = 0

Reorder the terms:
4 + 3i = 0

Solving
4 + 3i = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3i = 0 + -4
3i = 0 + -4

Combine like terms: 0 + -4 = -4
3i = -4

Divide each side by '3'.
i = -1.333333333

Simplifying
i = -1.333333333

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 = {-1.333333333, -8}

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