48k^2-6k=42

Solution for 48k^2-6k=42 equation:

Simplifying
48k2 + -6k = 42

Reorder the terms:
-6k + 48k2 = 42

Solving
-6k + 48k2 = 42

Solving for variable 'k'.

Reorder the terms:
-42 + -6k + 48k2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + -6k + 48k2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-7 + -1k + 8k2) = 0

Factor a trinomial.
6((-7 + -8k)(1 + -1k)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-7 + -8k)' equal to zero and attempt to solve:

Simplifying
-7 + -8k = 0

Solving
-7 + -8k = 0

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

Add '7' to each side of the equation.
-7 + 7 + -8k = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -8k = 0 + 7
-8k = 0 + 7

Combine like terms: 0 + 7 = 7
-8k = 7

Divide each side by '-8'.
k = -0.875

Simplifying
k = -0.875
Subproblem 2
Set the factor '(1 + -1k)' equal to zero and attempt to solve:

Simplifying
1 + -1k = 0

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

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

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

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

Simplifying
k = 1
Solution
k = {-0.875, 1}