3p^2+5p+2=0

Solution for 3p^2+5p+2=0 equation:

Simplifying
3p2 + 5p + 2 = 0

Reorder the terms:
2 + 5p + 3p2 = 0

Solving
2 + 5p + 3p2 = 0

Solving for variable 'p'.

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

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

Simplifying
1 + p = 0

Solving
1 + p = 0

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

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

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

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

Simplifying
p = -1
Subproblem 2
Set the factor '(2 + 3p)' equal to zero and attempt to solve:

Simplifying
2 + 3p = 0

Solving
2 + 3p = 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 + 3p = 0 + -2

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

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

Divide each side by '3'.
p = -0.6666666667

Simplifying
p = -0.6666666667
Solution
p = {-1, -0.6666666667}