4z^2+17z+15=0

Solution for 4z^2+17z+15=0 equation:

Simplifying
4z2 + 17z + 15 = 0

Reorder the terms:
15 + 17z + 4z2 = 0

Solving
15 + 17z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z)(5 + 4z) = 0

Subproblem 1
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 0

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

Add '-3' to each side of the equation.
3 + -3 + z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + z = 0 + -3
z = 0 + -3

Combine like terms: 0 + -3 = -3
z = -3

Simplifying
z = -3
Subproblem 2
Set the factor '(5 + 4z)' equal to zero and attempt to solve:

Simplifying
5 + 4z = 0

Solving
5 + 4z = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4z = 0 + -5
4z = 0 + -5

Combine like terms: 0 + -5 = -5
4z = -5

Divide each side by '4'.
z = -1.25

Simplifying
z = -1.25
Solution
z = {-3, -1.25}