4k^2-k-3=0

Solution for 4k^2-k-3=0 equation:

Simplifying
4k2 + -1k + -3 = 0

Reorder the terms:
-3 + -1k + 4k2 = 0

Solving
-3 + -1k + 4k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-3 + -4k)(1 + -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 '(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
Solution
k = {-0.75, 1}