8k^2+5k=2k^2+4

Solution for 8k^2+5k=2k^2+4 equation:

Simplifying
8k2 + 5k = 2k2 + 4

Reorder the terms:
5k + 8k2 = 2k2 + 4

Reorder the terms:
5k + 8k2 = 4 + 2k2

Solving
5k + 8k2 = 4 + 2k2

Solving for variable 'k'.

Reorder the terms:
-4 + 5k + 8k2 + -2k2 = 4 + 2k2 + -4 + -2k2

Combine like terms: 8k2 + -2k2 = 6k2
-4 + 5k + 6k2 = 4 + 2k2 + -4 + -2k2

Reorder the terms:
-4 + 5k + 6k2 = 4 + -4 + 2k2 + -2k2

Combine like terms: 4 + -4 = 0
-4 + 5k + 6k2 = 0 + 2k2 + -2k2
-4 + 5k + 6k2 = 2k2 + -2k2

Combine like terms: 2k2 + -2k2 = 0
-4 + 5k + 6k2 = 0

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

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

Simplifying
-4 + -3k = 0

Solving
-4 + -3k = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3k = 0 + 4

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

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

Divide each side by '-3'.
k = -1.333333333

Simplifying
k = -1.333333333
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 = {-1.333333333, 0.5}