45k^2+101k+48=k-5k^2

Solution for 45k^2+101k+48=k-5k^2 equation:

Simplifying
45k2 + 101k + 48 = k + -5k2

Reorder the terms:
48 + 101k + 45k2 = k + -5k2

Solving
48 + 101k + 45k2 = k + -5k2

Solving for variable 'k'.

Reorder the terms:
48 + 101k + -1k + 45k2 + 5k2 = k + -5k2 + -1k + 5k2

Combine like terms: 101k + -1k = 100k
48 + 100k + 45k2 + 5k2 = k + -5k2 + -1k + 5k2

Combine like terms: 45k2 + 5k2 = 50k2
48 + 100k + 50k2 = k + -5k2 + -1k + 5k2

Reorder the terms:
48 + 100k + 50k2 = k + -1k + -5k2 + 5k2

Combine like terms: k + -1k = 0
48 + 100k + 50k2 = 0 + -5k2 + 5k2
48 + 100k + 50k2 = -5k2 + 5k2

Combine like terms: -5k2 + 5k2 = 0
48 + 100k + 50k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 50k + 25k2) = 0

Factor a trinomial.
2((6 + 5k)(4 + 5k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 5k)' equal to zero and attempt to solve:

Simplifying
6 + 5k = 0

Solving
6 + 5k = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5k = 0 + -6
5k = 0 + -6

Combine like terms: 0 + -6 = -6
5k = -6

Divide each side by '5'.
k = -1.2

Simplifying
k = -1.2
Subproblem 2
Set the factor '(4 + 5k)' equal to zero and attempt to solve:

Simplifying
4 + 5k = 0

Solving
4 + 5k = 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 + 5k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5k = 0 + -4
5k = 0 + -4

Combine like terms: 0 + -4 = -4
5k = -4

Divide each side by '5'.
k = -0.8

Simplifying
k = -0.8
Solution
k = {-1.2, -0.8}