4k^2=11k-6

Solution for 4k^2=11k-6 equation:

Simplifying
4k2 = 11k + -6

Reorder the terms:
4k2 = -6 + 11k

Solving
4k2 = -6 + 11k

Solving for variable 'k'.

Reorder the terms:
6 + -11k + 4k2 = -6 + 11k + 6 + -11k

Reorder the terms:
6 + -11k + 4k2 = -6 + 6 + 11k + -11k

Combine like terms: -6 + 6 = 0
6 + -11k + 4k2 = 0 + 11k + -11k
6 + -11k + 4k2 = 11k + -11k

Combine like terms: 11k + -11k = 0
6 + -11k + 4k2 = 0

Factor a trinomial.
(3 + -4k)(2 + -1k) = 0

Subproblem 1
Set the factor '(3 + -4k)' equal to zero and attempt to solve:

Simplifying
3 + -4k = 0

Solving
3 + -4k = 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 + -4k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4k = 0 + -3
-4k = 0 + -3

Combine like terms: 0 + -3 = -3
-4k = -3

Divide each side by '-4'.
k = 0.75

Simplifying
k = 0.75
Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Solution
k = {0.75, 2}