2v^2+4v-42=0

Solution for 2v^2+4v-42=0 equation:

Simplifying
2v2 + 4v + -42 = 0

Reorder the terms:
-42 + 4v + 2v2 = 0

Solving
-42 + 4v + 2v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 2v + v2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + 2v + v2)' equal to zero and attempt to solve:

Simplifying
-21 + 2v + v2 = 0

Solving
-21 + 2v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 2v + 21 + v2 = 0 + 21

Reorder the terms:
-21 + 21 + 2v + v2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 2v + v2 = 0 + 21
2v + v2 = 0 + 21

Combine like terms: 0 + 21 = 21
2v + v2 = 21

The v term is 2v.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2v + 1 + v2 = 21 + 1

Reorder the terms:
1 + 2v + v2 = 21 + 1

Combine like terms: 21 + 1 = 22
1 + 2v + v2 = 22

Factor a perfect square on the left side:
(v + 1)(v + 1) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(v + 1) equal to 4.69041576 and -4.69041576.

Subproblem 1
v + 1 = 4.69041576

Simplifying
v + 1 = 4.69041576

Reorder the terms:
1 + v = 4.69041576

Solving
1 + v = 4.69041576

Solving for variable 'v'.

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

Add '-1' to each side of the equation.
1 + -1 + v = 4.69041576 + -1

Combine like terms: 1 + -1 = 0
0 + v = 4.69041576 + -1
v = 4.69041576 + -1

Combine like terms: 4.69041576 + -1 = 3.69041576
v = 3.69041576

Simplifying
v = 3.69041576

Subproblem 2
v + 1 = -4.69041576

Simplifying
v + 1 = -4.69041576

Reorder the terms:
1 + v = -4.69041576

Solving
1 + v = -4.69041576

Solving for variable 'v'.

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

Add '-1' to each side of the equation.
1 + -1 + v = -4.69041576 + -1

Combine like terms: 1 + -1 = 0
0 + v = -4.69041576 + -1
v = -4.69041576 + -1

Combine like terms: -4.69041576 + -1 = -5.69041576
v = -5.69041576

Simplifying
v = -5.69041576

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {3.69041576, -5.69041576}
Solution
v = {3.69041576, -5.69041576}