4p^2+11p+6=0

Solution for 4p^2+11p+6=0 equation:

Simplifying
4p2 + 11p + 6 = 0

Reorder the terms:
6 + 11p + 4p2 = 0

Solving
6 + 11p + 4p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(2 + p)(3 + 4p) = 0

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

Simplifying
2 + p = 0

Solving
2 + p = 0

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

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

Combine like terms: 2 + -2 = 0
0 + p = 0 + -2
p = 0 + -2

Combine like terms: 0 + -2 = -2
p = -2

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

Simplifying
3 + 4p = 0

Solving
3 + 4p = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4p = 0 + -3
4p = 0 + -3

Combine like terms: 0 + -3 = -3
4p = -3

Divide each side by '4'.
p = -0.75

Simplifying
p = -0.75
Solution
p = {-2, -0.75}