15p^2+54p+27=0

Solution for 15p^2+54p+27=0 equation:

Simplifying
15p2 + 54p + 27 = 0

Reorder the terms:
27 + 54p + 15p2 = 0

Solving
27 + 54p + 15p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 18p + 5p2) = 0

Factor a trinomial.
3((3 + p)(3 + 5p)) = 0

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

Simplifying
3 + p = 0

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

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

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

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

Simplifying
3 + 5p = 0

Solving
3 + 5p = 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 + 5p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5p = 0 + -3
5p = 0 + -3

Combine like terms: 0 + -3 = -3
5p = -3

Divide each side by '5'.
p = -0.6

Simplifying
p = -0.6
Solution
p = {-3, -0.6}