7v^2+7v-140=0

Solution for 7v^2+7v-140=0 equation:

Simplifying
7v2 + 7v + -140 = 0

Reorder the terms:
-140 + 7v + 7v2 = 0

Solving
-140 + 7v + 7v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-20 + v + v2) = 0

Factor a trinomial.
7((-5 + -1v)(4 + -1v)) = 0

Ignore the factor 7.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Solution
v = {-5, 4}