(3p+1)(9p-1)=

Solution for (3p+1)(9p-1)= equation:

Simplifying
(3p + 1)(9p + -1) = 0

Reorder the terms:
(1 + 3p)(9p + -1) = 0

Reorder the terms:
(1 + 3p)(-1 + 9p) = 0

Multiply (1 + 3p) * (-1 + 9p)
(1(-1 + 9p) + 3p * (-1 + 9p)) = 0
((-1 * 1 + 9p * 1) + 3p * (-1 + 9p)) = 0
((-1 + 9p) + 3p * (-1 + 9p)) = 0
(-1 + 9p + (-1 * 3p + 9p * 3p)) = 0
(-1 + 9p + (-3p + 27p2)) = 0

Combine like terms: 9p + -3p = 6p
(-1 + 6p + 27p2) = 0

Solving
-1 + 6p + 27p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-1 + -3p)(1 + -9p) = 0

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

Simplifying
-1 + -3p = 0

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

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

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

Divide each side by '-3'.
p = -0.3333333333

Simplifying
p = -0.3333333333
Subproblem 2
Set the factor '(1 + -9p)' equal to zero and attempt to solve:

Simplifying
1 + -9p = 0

Solving
1 + -9p = 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 + -9p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -9p = 0 + -1
-9p = 0 + -1

Combine like terms: 0 + -1 = -1
-9p = -1

Divide each side by '-9'.
p = 0.1111111111

Simplifying
p = 0.1111111111
Solution
p = {-0.3333333333, 0.1111111111}