4v^2+29v+45=0

Solution for 4v^2+29v+45=0 equation:

Simplifying
4v2 + 29v + 45 = 0

Reorder the terms:
45 + 29v + 4v2 = 0

Solving
45 + 29v + 4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(5 + v)(9 + 4v) = 0

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

Simplifying
5 + v = 0

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

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

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

Simplifying
v = -5
Subproblem 2
Set the factor '(9 + 4v)' equal to zero and attempt to solve:

Simplifying
9 + 4v = 0

Solving
9 + 4v = 0

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

Add '-9' to each side of the equation.
9 + -9 + 4v = 0 + -9

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

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

Divide each side by '4'.
v = -2.25

Simplifying
v = -2.25
Solution
v = {-5, -2.25}