4k^2-4k-6=-3

Solution for 4k^2-4k-6=-3 equation:

Simplifying
4k2 + -4k + -6 = -3

Reorder the terms:
-6 + -4k + 4k2 = -3

Solving
-6 + -4k + 4k2 = -3

Solving for variable 'k'.

Reorder the terms:
-6 + 3 + -4k + 4k2 = -3 + 3

Combine like terms: -6 + 3 = -3
-3 + -4k + 4k2 = -3 + 3

Combine like terms: -3 + 3 = 0
-3 + -4k + 4k2 = 0

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

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

Simplifying
-1 + -2k = 0

Solving
-1 + -2k = 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 + -2k = 0 + 1

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

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

Divide each side by '-2'.
k = -0.5

Simplifying
k = -0.5
Subproblem 2
Set the factor '(3 + -2k)' equal to zero and attempt to solve:

Simplifying
3 + -2k = 0

Solving
3 + -2k = 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 + -2k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2k = 0 + -3
-2k = 0 + -3

Combine like terms: 0 + -3 = -3
-2k = -3

Divide each side by '-2'.
k = 1.5

Simplifying
k = 1.5
Solution
k = {-0.5, 1.5}