4v^2+15v+1=5

Solution for 4v^2+15v+1=5 equation:

Simplifying
4v2 + 15v + 1 = 5

Reorder the terms:
1 + 15v + 4v2 = 5

Solving
1 + 15v + 4v2 = 5

Solving for variable 'v'.

Reorder the terms:
1 + -5 + 15v + 4v2 = 5 + -5

Combine like terms: 1 + -5 = -4
-4 + 15v + 4v2 = 5 + -5

Combine like terms: 5 + -5 = 0
-4 + 15v + 4v2 = 0

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

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 '(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
Solution
v = {-4, 0.25}