100k=48-28k^2

Solution for 100k=48-28k^2 equation:

Simplifying
100k = 48 + -28k2

Solving
100k = 48 + -28k2

Solving for variable 'k'.

Reorder the terms:
-48 + 100k + 28k2 = 48 + -28k2 + -48 + 28k2

Reorder the terms:
-48 + 100k + 28k2 = 48 + -48 + -28k2 + 28k2

Combine like terms: 48 + -48 = 0
-48 + 100k + 28k2 = 0 + -28k2 + 28k2
-48 + 100k + 28k2 = -28k2 + 28k2

Combine like terms: -28k2 + 28k2 = 0
-48 + 100k + 28k2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + 25k + 7k2) = 0

Factor a trinomial.
4((-4 + -1k)(3 + -7k)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + -7k)' equal to zero and attempt to solve:

Simplifying
3 + -7k = 0

Solving
3 + -7k = 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 + -7k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7k = 0 + -3
-7k = 0 + -3

Combine like terms: 0 + -3 = -3
-7k = -3

Divide each side by '-7'.
k = 0.4285714286

Simplifying
k = 0.4285714286
Solution
k = {-4, 0.4285714286}