11p^2(2p+1)-22p(2p+1)=0

Solution for 11p^2(2p+1)-22p(2p+1)=0 equation:

Simplifying
11p2(2p + 1) + -22p(2p + 1) = 0

Reorder the terms:
11p2(1 + 2p) + -22p(2p + 1) = 0
(1 * 11p2 + 2p * 11p2) + -22p(2p + 1) = 0
(11p2 + 22p3) + -22p(2p + 1) = 0

Reorder the terms:
11p2 + 22p3 + -22p(1 + 2p) = 0
11p2 + 22p3 + (1 * -22p + 2p * -22p) = 0
11p2 + 22p3 + (-22p + -44p2) = 0

Reorder the terms:
-22p + 11p2 + -44p2 + 22p3 = 0

Combine like terms: 11p2 + -44p2 = -33p2
-22p + -33p2 + 22p3 = 0

Solving
-22p + -33p2 + 22p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '11p'.
11p(-2 + -3p + 2p2) = 0

Factor a trinomial.
11p((-1 + -2p)(2 + -1p)) = 0

Ignore the factor 11.
Subproblem 1
Set the factor 'p' equal to zero and attempt to solve:

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0
Subproblem 2
Set the factor '(-1 + -2p)' equal to zero and attempt to solve:

Simplifying
-1 + -2p = 0

Solving
-1 + -2p = 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 + -2p = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2p = 0 + 1
-2p = 0 + 1

Combine like terms: 0 + 1 = 1
-2p = 1

Divide each side by '-2'.
p = -0.5

Simplifying
p = -0.5
Subproblem 3
Set the factor '(2 + -1p)' equal to zero and attempt to solve:

Simplifying
2 + -1p = 0

Solving
2 + -1p = 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 + -1p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1p = 0 + -2
-1p = 0 + -2

Combine like terms: 0 + -2 = -2
-1p = -2

Divide each side by '-1'.
p = 2

Simplifying
p = 2
Solution
p = {0, -0.5, 2}