54p^2+45p-54=0

Solution for 54p^2+45p-54=0 equation:

Simplifying
54p2 + 45p + -54 = 0

Reorder the terms:
-54 + 45p + 54p2 = 0

Solving
-54 + 45p + 54p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-6 + 5p + 6p2) = 0

Factor a trinomial.
9((-3 + -2p)(2 + -3p)) = 0

Ignore the factor 9.
Subproblem 1
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
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 = {-1.5, 0.6666666667}