4q^2+25q+6=0

Solution for 4q^2+25q+6=0 equation:

Simplifying
4q2 + 25q + 6 = 0

Reorder the terms:
6 + 25q + 4q2 = 0

Solving
6 + 25q + 4q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(6 + q)(1 + 4q) = 0

Subproblem 1
Set the factor '(6 + q)' equal to zero and attempt to solve:

Simplifying
6 + q = 0

Solving
6 + q = 0

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

Add '-6' to each side of the equation.
6 + -6 + q = 0 + -6

Combine like terms: 6 + -6 = 0
0 + q = 0 + -6
q = 0 + -6

Combine like terms: 0 + -6 = -6
q = -6

Simplifying
q = -6
Subproblem 2
Set the factor '(1 + 4q)' equal to zero and attempt to solve:

Simplifying
1 + 4q = 0

Solving
1 + 4q = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4q = 0 + -1
4q = 0 + -1

Combine like terms: 0 + -1 = -1
4q = -1

Divide each side by '4'.
q = -0.25

Simplifying
q = -0.25
Solution
q = {-6, -0.25}