4k^2-8k-21=0

Solution for 4k^2-8k-21=0 equation:

Simplifying
4k2 + -8k + -21 = 0

Reorder the terms:
-21 + -8k + 4k2 = 0

Solving
-21 + -8k + 4k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-3 + -2k)(7 + -2k) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -2k)' equal to zero and attempt to solve:

Simplifying
7 + -2k = 0

Solving
7 + -2k = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2k = 0 + -7
-2k = 0 + -7

Combine like terms: 0 + -7 = -7
-2k = -7

Divide each side by '-2'.
k = 3.5

Simplifying
k = 3.5
Solution
k = {-1.5, 3.5}