7v^2-63v+140=0

Solution for 7v^2-63v+140=0 equation:

Simplifying
7v2 + -63v + 140 = 0

Reorder the terms:
140 + -63v + 7v2 = 0

Solving
140 + -63v + 7v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '7'.
7(20 + -9v + v2) = 0

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

Ignore the factor 7.
Subproblem 1
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
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 = {4, 5}