4q^2+16q+15=0

Solution for 4q^2+16q+15=0 equation:

Simplifying
4q2 + 16q + 15 = 0

Reorder the terms:
15 + 16q + 4q2 = 0

Solving
15 + 16q + 4q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(5 + 2q)(3 + 2q) = 0

Subproblem 1
Set the factor '(5 + 2q)' equal to zero and attempt to solve:

Simplifying
5 + 2q = 0

Solving
5 + 2q = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2q = 0 + -5
2q = 0 + -5

Combine like terms: 0 + -5 = -5
2q = -5

Divide each side by '2'.
q = -2.5

Simplifying
q = -2.5
Subproblem 2
Set the factor '(3 + 2q)' equal to zero and attempt to solve:

Simplifying
3 + 2q = 0

Solving
3 + 2q = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2q = 0 + -3
2q = 0 + -3

Combine like terms: 0 + -3 = -3
2q = -3

Divide each side by '2'.
q = -1.5

Simplifying
q = -1.5
Solution
q = {-2.5, -1.5}