4p^2+13p+9=0

Solution for 4p^2+13p+9=0 equation:

Simplifying
4p2 + 13p + 9 = 0

Reorder the terms:
9 + 13p + 4p2 = 0

Solving
9 + 13p + 4p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(9 + 4p)(1 + p) = 0

Subproblem 1
Set the factor '(9 + 4p)' equal to zero and attempt to solve:

Simplifying
9 + 4p = 0

Solving
9 + 4p = 0

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

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

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

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

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

Simplifying
p = -2.25
Subproblem 2
Set the factor '(1 + p)' equal to zero and attempt to solve:

Simplifying
1 + p = 0

Solving
1 + p = 0

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

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

Combine like terms: 1 + -1 = 0
0 + p = 0 + -1
p = 0 + -1

Combine like terms: 0 + -1 = -1
p = -1

Simplifying
p = -1
Solution
p = {-2.25, -1}