3v^2+15v-48=-6

Solution for 3v^2+15v-48=-6 equation:

Simplifying
3v2 + 15v + -48 = -6

Reorder the terms:
-48 + 15v + 3v2 = -6

Solving
-48 + 15v + 3v2 = -6

Solving for variable 'v'.

Reorder the terms:
-48 + 6 + 15v + 3v2 = -6 + 6

Combine like terms: -48 + 6 = -42
-42 + 15v + 3v2 = -6 + 6

Combine like terms: -6 + 6 = 0
-42 + 15v + 3v2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 5v + v2) = 0

Factor a trinomial.
3((-7 + -1v)(2 + -1v)) = 0

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

Simplifying
2 + -1v = 0

Solving
2 + -1v = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1v = 0 + -2
-1v = 0 + -2

Combine like terms: 0 + -2 = -2
-1v = -2

Divide each side by '-1'.
v = 2

Simplifying
v = 2
Solution
v = {-7, 2}