35v^2=21+98v

Solution for 35v^2=21+98v equation:

Simplifying
35v2 = 21 + 98v

Solving
35v2 = 21 + 98v

Solving for variable 'v'.

Reorder the terms:
-21 + -98v + 35v2 = 21 + 98v + -21 + -98v

Reorder the terms:
-21 + -98v + 35v2 = 21 + -21 + 98v + -98v

Combine like terms: 21 + -21 = 0
-21 + -98v + 35v2 = 0 + 98v + -98v
-21 + -98v + 35v2 = 98v + -98v

Combine like terms: 98v + -98v = 0
-21 + -98v + 35v2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-3 + -14v + 5v2) = 0

Factor a trinomial.
7((-1 + -5v)(3 + -1v)) = 0

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

Simplifying
-1 + -5v = 0

Solving
-1 + -5v = 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 + -5v = 0 + 1

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

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

Divide each side by '-5'.
v = -0.2

Simplifying
v = -0.2
Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3
Solution
v = {-0.2, 3}