14v^2+21v-35=0

Solution for 14v^2+21v-35=0 equation:

Simplifying
14v2 + 21v + -35 = 0

Reorder the terms:
-35 + 21v + 14v2 = 0

Solving
-35 + 21v + 14v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-5 + 3v + 2v2) = 0

Factor a trinomial.
7((-5 + -2v)(1 + -1v)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-5 + -2v)' equal to zero and attempt to solve:

Simplifying
-5 + -2v = 0

Solving
-5 + -2v = 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 + -2v = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2v = 0 + 5
-2v = 0 + 5

Combine like terms: 0 + 5 = 5
-2v = 5

Divide each side by '-2'.
v = -2.5

Simplifying
v = -2.5
Subproblem 2
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
Solution
v = {-2.5, 1}