4k^2=-3-8k

Solution for 4k^2=-3-8k equation:

Simplifying
4k2 = -3 + -8k

Solving
4k2 = -3 + -8k

Solving for variable 'k'.

Reorder the terms:
3 + 8k + 4k2 = -3 + -8k + 3 + 8k

Reorder the terms:
3 + 8k + 4k2 = -3 + 3 + -8k + 8k

Combine like terms: -3 + 3 = 0
3 + 8k + 4k2 = 0 + -8k + 8k
3 + 8k + 4k2 = -8k + 8k

Combine like terms: -8k + 8k = 0
3 + 8k + 4k2 = 0

Factor a trinomial.
(3 + 2k)(1 + 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 '(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
Solution
k = {-1.5, -0.5}