(5x-1)k=(2x+8)k

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Solution for (5x-1)k=(2x+8)k equation: 


Simplifying
(5x + -1) * k = (2x + 8) * k

Reorder the terms:
(-1 + 5x) * k = (2x + 8) * k

Reorder the terms for easier multiplication:
k(-1 + 5x) = (2x + 8) * k
(-1 * k + 5x * k) = (2x + 8) * k
(-1k + 5kx) = (2x + 8) * k

Reorder the terms:
-1k + 5kx = (8 + 2x) * k

Reorder the terms for easier multiplication:
-1k + 5kx = k(8 + 2x)
-1k + 5kx = (8 * k + 2x * k)
-1k + 5kx = (8k + 2kx)

Solving
-1k + 5kx = 8k + 2kx

Solving for variable 'k'.

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

Add '-8k' to each side of the equation.
-1k + -8k + 5kx = 8k + -8k + 2kx

Combine like terms: -1k + -8k = -9k
-9k + 5kx = 8k + -8k + 2kx

Combine like terms: 8k + -8k = 0
-9k + 5kx = 0 + 2kx
-9k + 5kx = 2kx

Add '-2kx' to each side of the equation.
-9k + 5kx + -2kx = 2kx + -2kx

Combine like terms: 5kx + -2kx = 3kx
-9k + 3kx = 2kx + -2kx

Combine like terms: 2kx + -2kx = 0
-9k + 3kx = 0

Factor out the Greatest Common Factor (GCF), '3k'.
3k(-3 + x) = 0

Ignore the factor 3.

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

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0

Subproblem 2
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

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

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Add '-1x' to each side of the equation.
x + -1x = 3 + -1x

Combine like terms: x + -1x = 0
0 = 3 + -1x

Simplifying
0 = 3 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
k = {0}

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