2k^2+6=7k

Solution for 2k^2+6=7k equation:

Simplifying
2k2 + 6 = 7k

Reorder the terms:
6 + 2k2 = 7k

Solving
6 + 2k2 = 7k

Solving for variable 'k'.

Reorder the terms:
6 + -7k + 2k2 = 7k + -7k

Combine like terms: 7k + -7k = 0
6 + -7k + 2k2 = 0

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