43k^2+56k=3k^2+48

Solution for 43k^2+56k=3k^2+48 equation:

Simplifying
43k2 + 56k = 3k2 + 48

Reorder the terms:
56k + 43k2 = 3k2 + 48

Reorder the terms:
56k + 43k2 = 48 + 3k2

Solving
56k + 43k2 = 48 + 3k2

Solving for variable 'k'.

Reorder the terms:
-48 + 56k + 43k2 + -3k2 = 48 + 3k2 + -48 + -3k2

Combine like terms: 43k2 + -3k2 = 40k2
-48 + 56k + 40k2 = 48 + 3k2 + -48 + -3k2

Reorder the terms:
-48 + 56k + 40k2 = 48 + -48 + 3k2 + -3k2

Combine like terms: 48 + -48 = 0
-48 + 56k + 40k2 = 0 + 3k2 + -3k2
-48 + 56k + 40k2 = 3k2 + -3k2

Combine like terms: 3k2 + -3k2 = 0
-48 + 56k + 40k2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-6 + 7k + 5k2) = 0

Factor a trinomial.
8((-2 + -1k)(3 + -5k)) = 0

Ignore the factor 8.
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 '(3 + -5k)' equal to zero and attempt to solve:

Simplifying
3 + -5k = 0

Solving
3 + -5k = 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 + -5k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5k = 0 + -3
-5k = 0 + -3

Combine like terms: 0 + -3 = -3
-5k = -3

Divide each side by '-5'.
k = 0.6

Simplifying
k = 0.6
Solution
k = {-2, 0.6}