v^2+12v-42=3

Solution for v^2+12v-42=3 equation:

Simplifying
v2 + 12v + -42 = 3

Reorder the terms:
-42 + 12v + v2 = 3

Solving
-42 + 12v + v2 = 3

Solving for variable 'v'.

Reorder the terms:
-42 + -3 + 12v + v2 = 3 + -3

Combine like terms: -42 + -3 = -45
-45 + 12v + v2 = 3 + -3

Combine like terms: 3 + -3 = 0
-45 + 12v + v2 = 0

Factor a trinomial.
(-15 + -1v)(3 + -1v) = 0

Subproblem 1
Set the factor '(-15 + -1v)' equal to zero and attempt to solve:

Simplifying
-15 + -1v = 0

Solving
-15 + -1v = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1v = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1v = 0 + 15
-1v = 0 + 15

Combine like terms: 0 + 15 = 15
-1v = 15

Divide each side by '-1'.
v = -15

Simplifying
v = -15
Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3
Solution
v = {-15, 3}