k^2-k+8=6k-4

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Solution for k^2-k+8=6k-4 equation:


Simplifying
k2 + -1k + 8 = 6k + -4

Reorder the terms:
8 + -1k + k2 = 6k + -4

Reorder the terms:
8 + -1k + k2 = -4 + 6k

Solving
8 + -1k + k2 = -4 + 6k

Solving for variable 'k'.

Reorder the terms:
8 + 4 + -1k + -6k + k2 = -4 + 6k + 4 + -6k

Combine like terms: 8 + 4 = 12
12 + -1k + -6k + k2 = -4 + 6k + 4 + -6k

Combine like terms: -1k + -6k = -7k
12 + -7k + k2 = -4 + 6k + 4 + -6k

Reorder the terms:
12 + -7k + k2 = -4 + 4 + 6k + -6k

Combine like terms: -4 + 4 = 0
12 + -7k + k2 = 0 + 6k + -6k
12 + -7k + k2 = 6k + -6k

Combine like terms: 6k + -6k = 0
12 + -7k + k2 = 0

Factor a trinomial.
(3 + -1k)(4 + -1k) = 0


Subproblem 1
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 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 + -1k = 0 + -3

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

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

Divide each side by '-1'.
k = 3

Simplifying
k = 3

Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {3, 4}

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