=7v^2+35v-42

Solution for =7v^2+35v-42 equation:

Simplifying
0 = 7v2 + 35v + -42

Reorder the terms:
0 = -42 + 35v + 7v2

Solving
0 = -42 + 35v + 7v2

Solving for variable 'v'.

Combine like terms: 0 + 42 = 42
42 + -35v + -7v2 = -42 + 35v + 7v2 + 42 + -35v + -7v2

Reorder the terms:
42 + -35v + -7v2 = -42 + 42 + 35v + -35v + 7v2 + -7v2

Combine like terms: -42 + 42 = 0
42 + -35v + -7v2 = 0 + 35v + -35v + 7v2 + -7v2
42 + -35v + -7v2 = 35v + -35v + 7v2 + -7v2

Combine like terms: 35v + -35v = 0
42 + -35v + -7v2 = 0 + 7v2 + -7v2
42 + -35v + -7v2 = 7v2 + -7v2

Combine like terms: 7v2 + -7v2 = 0
42 + -35v + -7v2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(6 + -5v + -1v2) = 0

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

Ignore the factor 7.
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 '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 0

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

Add '-6' to each side of the equation.
6 + -6 + v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + v = 0 + -6
v = 0 + -6

Combine like terms: 0 + -6 = -6
v = -6

Simplifying
v = -6
Solution
v = {1, -6}