12p(1-p)=1.92

Solution for 12p(1-p)=1.92 equation:

Simplifying
12p(1 + -1p) = 1.92
(1 * 12p + -1p * 12p) = 1.92
(12p + -12p2) = 1.92

Solving
12p + -12p2 = 1.92

Solving for variable 'p'.

Reorder the terms:
-1.92 + 12p + -12p2 = 1.92 + -1.92

Combine like terms: 1.92 + -1.92 = 0.00
-1.92 + 12p + -12p2 = 0.00

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
0.16 + -1p + p2 = 0.00

Move the constant term to the right:

Add '-0.16' to each side of the equation.
0.16 + -1p + -0.16 + p2 = 0.00 + -0.16

Reorder the terms:
0.16 + -0.16 + -1p + p2 = 0.00 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
0.00 + -1p + p2 = 0.00 + -0.16
-1p + p2 = 0.00 + -0.16

Combine like terms: 0.00 + -0.16 = -0.16
-1p + p2 = -0.16

The p term is -1p.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1p + 0.25 + p2 = -0.16 + 0.25

Reorder the terms:
0.25 + -1p + p2 = -0.16 + 0.25

Combine like terms: -0.16 + 0.25 = 0.09
0.25 + -1p + p2 = 0.09

Factor a perfect square on the left side:
(p + -0.5)(p + -0.5) = 0.09

Calculate the square root of the right side: 0.3

Break this problem into two subproblems by setting 
(p + -0.5) equal to 0.3 and -0.3.

Subproblem 1
p + -0.5 = 0.3

Simplifying
p + -0.5 = 0.3

Reorder the terms:
-0.5 + p = 0.3

Solving
-0.5 + p = 0.3

Solving for variable 'p'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + p = 0.3 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + p = 0.3 + 0.5
p = 0.3 + 0.5

Combine like terms: 0.3 + 0.5 = 0.8
p = 0.8

Simplifying
p = 0.8

Subproblem 2
p + -0.5 = -0.3

Simplifying
p + -0.5 = -0.3

Reorder the terms:
-0.5 + p = -0.3

Solving
-0.5 + p = -0.3

Solving for variable 'p'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + p = -0.3 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + p = -0.3 + 0.5
p = -0.3 + 0.5

Combine like terms: -0.3 + 0.5 = 0.2
p = 0.2

Simplifying
p = 0.2

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.8, 0.2}