4v^2+3=13v

Solution for 4v^2+3=13v equation:

Simplifying
4v2 + 3 = 13v

Reorder the terms:
3 + 4v2 = 13v

Solving
3 + 4v2 = 13v

Solving for variable 'v'.

Reorder the terms:
3 + -13v + 4v2 = 13v + -13v

Combine like terms: 13v + -13v = 0
3 + -13v + 4v2 = 0

Factor a trinomial.
(1 + -4v)(3 + -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 '(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 = {0.25, 3}