7v^2+7v-210=0

Solution for 7v^2+7v-210=0 equation:

Simplifying
7v2 + 7v + -210 = 0

Reorder the terms:
-210 + 7v + 7v2 = 0

Solving
-210 + 7v + 7v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-30 + v + v2) = 0

Factor a trinomial.
7((-6 + -1v)(5 + -1v)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-6 + -1v)' equal to zero and attempt to solve:

Simplifying
-6 + -1v = 0

Solving
-6 + -1v = 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 + -1v = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1v = 0 + 6
-1v = 0 + 6

Combine like terms: 0 + 6 = 6
-1v = 6

Divide each side by '-1'.
v = -6

Simplifying
v = -6
Subproblem 2
Set the factor '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5
Solution
v = {-6, 5}