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

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


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

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

Multiply (4 + -8i) * (8 + i)
x(4(8 + i) + -8i * (8 + i)) = 0
x((8 * 4 + i * 4) + -8i * (8 + i)) = 0
x((32 + 4i) + -8i * (8 + i)) = 0
x(32 + 4i + (8 * -8i + i * -8i)) = 0
x(32 + 4i + (-64i + -8i2)) = 0

Combine like terms: 4i + -64i = -60i
x(32 + -60i + -8i2) = 0
(32 * x + -60i * x + -8i2 * x) = 0

Reorder the terms:
(-60ix + -8i2x + 32x) = 0
(-60ix + -8i2x + 32x) = 0

Solving
-60ix + -8i2x + 32x = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-15i + -2i2 + 8) = 0

Factor a trinomial.
4x((-1i + -8)(2i + -1)) = 0

Ignore the factor 4.

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 '(-1i + -8)' equal to zero and attempt to solve: Simplifying -1i + -8 = 0 Reorder the terms: -8 + -1i = 0 Solving -8 + -1i = 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 + -1i = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1i = 0 + 8 -1i = 0 + 8 Combine like terms: 0 + 8 = 8 -1i = 8 Divide each side by '-1'. i = -8 Simplifying i = -8

Subproblem 3

Set the factor '(2i + -1)' equal to zero and attempt to solve: Simplifying 2i + -1 = 0 Reorder the terms: -1 + 2i = 0 Solving -1 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 2i = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2i = 0 + 1 2i = 0 + 1 Combine like terms: 0 + 1 = 1 2i = 1 Divide each side by '2'. i = 0.5 Simplifying i = 0.5

Solution

i = {-8, 0.5}

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