6v^2-48v=-42

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

Simplifying
6v2 + -48v = -42

Reorder the terms:
-48v + 6v2 = -42

Solving
-48v + 6v2 = -42

Solving for variable 'v'.

Reorder the terms:
42 + -48v + 6v2 = -42 + 42

Combine like terms: -42 + 42 = 0
42 + -48v + 6v2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(7 + -8v + v2) = 0

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

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

Simplifying
1 + -1v = 0

Solving
1 + -1v = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1v = 0 + -1

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

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

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

Simplifying
v = 1
Subproblem 2
Set the factor '(7 + -1v)' equal to zero and attempt to solve:

Simplifying
7 + -1v = 0

Solving
7 + -1v = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1v = 0 + -7
-1v = 0 + -7

Combine like terms: 0 + -7 = -7
-1v = -7

Divide each side by '-1'.
v = 7

Simplifying
v = 7
Solution
v = {1, 7}