4v^2+2=9v

Solution for 4v^2+2=9v equation:

Simplifying
4v2 + 2 = 9v

Reorder the terms:
2 + 4v2 = 9v

Solving
2 + 4v2 = 9v

Solving for variable 'v'.

Reorder the terms:
2 + -9v + 4v2 = 9v + -9v

Combine like terms: 9v + -9v = 0
2 + -9v + 4v2 = 0

Factor a trinomial.
(1 + -4v)(2 + -1v) = 0

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

Simplifying
1 + -4v = 0

Solving
1 + -4v = 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 + -4v = 0 + -1

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

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

Divide each side by '-4'.
v = 0.25

Simplifying
v = 0.25
Subproblem 2
Set the factor '(2 + -1v)' equal to zero and attempt to solve:

Simplifying
2 + -1v = 0

Solving
2 + -1v = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1v = 0 + -2
-1v = 0 + -2

Combine like terms: 0 + -2 = -2
-1v = -2

Divide each side by '-1'.
v = 2

Simplifying
v = 2
Solution
v = {0.25, 2}