4k^2-5k=51

Solution for 4k^2-5k=51 equation:

Simplifying
4k2 + -5k = 51

Reorder the terms:
-5k + 4k2 = 51

Solving
-5k + 4k2 = 51

Solving for variable 'k'.

Reorder the terms:
-51 + -5k + 4k2 = 51 + -51

Combine like terms: 51 + -51 = 0
-51 + -5k + 4k2 = 0

Factor a trinomial.
(-3 + -1k)(17 + -4k) = 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 '(17 + -4k)' equal to zero and attempt to solve:

Simplifying
17 + -4k = 0

Solving
17 + -4k = 0

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

Add '-17' to each side of the equation.
17 + -17 + -4k = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -4k = 0 + -17
-4k = 0 + -17

Combine like terms: 0 + -17 = -17
-4k = -17

Divide each side by '-4'.
k = 4.25

Simplifying
k = 4.25
Solution
k = {-3, 4.25}