4z^2+13z+9=0

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

Simplifying
4z2 + 13z + 9 = 0

Reorder the terms:
9 + 13z + 4z2 = 0

Solving
9 + 13z + 4z2 = 0

Solving for variable 'z'.

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

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

Simplifying
9 + 4z = 0

Solving
9 + 4z = 0

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

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

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

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

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

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

Simplifying
1 + z = 0

Solving
1 + z = 0

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

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

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

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

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