4k^2+6k=4

Solution for 4k^2+6k=4 equation:

Simplifying
4k2 + 6k = 4

Reorder the terms:
6k + 4k2 = 4

Solving
6k + 4k2 = 4

Solving for variable 'k'.

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 3k + 2k2) = 0

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

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

Simplifying
-2 + -1k = 0

Solving
-2 + -1k = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1k = 0 + 2

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

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

Divide each side by '-1'.
k = -2

Simplifying
k = -2
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 = {-2, 0.5}