2k^2-4=7k

Solution for 2k^2-4=7k equation:

Simplifying
2k2 + -4 = 7k

Reorder the terms:
-4 + 2k2 = 7k

Solving
-4 + 2k2 = 7k

Solving for variable 'k'.

Reorder the terms:
-4 + -7k + 2k2 = 7k + -7k

Combine like terms: 7k + -7k = 0
-4 + -7k + 2k2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 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 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {-0.5, 4}