4k^2-k=5

Solution for 4k^2-k=5 equation:

Simplifying
4k2 + -1k = 5

Reorder the terms:
-1k + 4k2 = 5

Solving
-1k + 4k2 = 5

Solving for variable 'k'.

Reorder the terms:
-5 + -1k + 4k2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -1k + 4k2 = 0

Factor a trinomial.
(-1 + -1k)(5 + -4k) = 0

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

Simplifying
-1 + -1k = 0

Solving
-1 + -1k = 0

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

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

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

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

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

Simplifying
k = -1
Subproblem 2
Set the factor '(5 + -4k)' equal to zero and attempt to solve:

Simplifying
5 + -4k = 0

Solving
5 + -4k = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4k = 0 + -5
-4k = 0 + -5

Combine like terms: 0 + -5 = -5
-4k = -5

Divide each side by '-4'.
k = 1.25

Simplifying
k = 1.25
Solution
k = {-1, 1.25}