6p^2+9p-27=0

Solution for 6p^2+9p-27=0 equation:

Simplifying
6p2 + 9p + -27 = 0

Reorder the terms:
-27 + 9p + 6p2 = 0

Solving
-27 + 9p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + 3p + 2p2) = 0

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

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

Simplifying
-3 + -1p = 0

Solving
-3 + -1p = 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 + -1p = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1p = 0 + 3
-1p = 0 + 3

Combine like terms: 0 + 3 = 3
-1p = 3

Divide each side by '-1'.
p = -3

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

Simplifying
3 + -2p = 0

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

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

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

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

Simplifying
p = 1.5
Solution
p = {-3, 1.5}