(9p+13)(9-3p)=0

Solution for (9p+13)(9-3p)=0 equation:

Simplifying
(9p + 13)(9 + -3p) = 0

Reorder the terms:
(13 + 9p)(9 + -3p) = 0

Multiply (13 + 9p) * (9 + -3p)
(13(9 + -3p) + 9p * (9 + -3p)) = 0
((9 * 13 + -3p * 13) + 9p * (9 + -3p)) = 0
((117 + -39p) + 9p * (9 + -3p)) = 0
(117 + -39p + (9 * 9p + -3p * 9p)) = 0
(117 + -39p + (81p + -27p2)) = 0

Combine like terms: -39p + 81p = 42p
(117 + 42p + -27p2) = 0

Solving
117 + 42p + -27p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(39 + 14p + -9p2) = 0

Factor a trinomial.
3((3 + -1p)(13 + 9p)) = 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 '(13 + 9p)' equal to zero and attempt to solve:

Simplifying
13 + 9p = 0

Solving
13 + 9p = 0

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

Add '-13' to each side of the equation.
13 + -13 + 9p = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 9p = 0 + -13
9p = 0 + -13

Combine like terms: 0 + -13 = -13
9p = -13

Divide each side by '9'.
p = -1.444444444

Simplifying
p = -1.444444444
Solution
p = {3, -1.444444444}