12=5x(1-x)21

Solution for 12=5x(1-x)21 equation:

Simplifying
12 = 5x(1 + -1x) * 21

Reorder the terms for easier multiplication:
12 = 5 * 21x(1 + -1x)

Multiply 5 * 21
12 = 105x(1 + -1x)
12 = (1 * 105x + -1x * 105x)
12 = (105x + -105x2)

Solving
12 = 105x + -105x2

Solving for variable 'x'.

Reorder the terms:
12 + -105x + 105x2 = 105x + -105x + -105x2 + 105x2

Combine like terms: 105x + -105x = 0
12 + -105x + 105x2 = 0 + -105x2 + 105x2
12 + -105x + 105x2 = -105x2 + 105x2

Combine like terms: -105x2 + 105x2 = 0
12 + -105x + 105x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -35x + 35x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + -35x + 35x2)' equal to zero and attempt to solve:

Simplifying
4 + -35x + 35x2 = 0

Solving
4 + -35x + 35x2 = 0

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

Divide each side by '35'.
0.1142857143 + -1x + x2 = 0

Move the constant term to the right:

Add '-0.1142857143' to each side of the equation.
0.1142857143 + -1x + -0.1142857143 + x2 = 0 + -0.1142857143

Reorder the terms:
0.1142857143 + -0.1142857143 + -1x + x2 = 0 + -0.1142857143

Combine like terms: 0.1142857143 + -0.1142857143 = 0.0000000000
0.0000000000 + -1x + x2 = 0 + -0.1142857143
-1x + x2 = 0 + -0.1142857143

Combine like terms: 0 + -0.1142857143 = -0.1142857143
-1x + x2 = -0.1142857143

The x term is -1x.  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.
-1x + 0.25 + x2 = -0.1142857143 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.1142857143 + 0.25

Combine like terms: -0.1142857143 + 0.25 = 0.1357142857
0.25 + -1x + x2 = 0.1357142857

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.1357142857

Calculate the square root of the right side: 0.368394199

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.368394199 and -0.368394199.

Subproblem 1
x + -0.5 = 0.368394199

Simplifying
x + -0.5 = 0.368394199

Reorder the terms:
-0.5 + x = 0.368394199

Solving
-0.5 + x = 0.368394199

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.368394199 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.368394199 + 0.5
x = 0.368394199 + 0.5

Combine like terms: 0.368394199 + 0.5 = 0.868394199
x = 0.868394199

Simplifying
x = 0.868394199

Subproblem 2
x + -0.5 = -0.368394199

Simplifying
x + -0.5 = -0.368394199

Reorder the terms:
-0.5 + x = -0.368394199

Solving
-0.5 + x = -0.368394199

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.368394199 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.368394199 + 0.5
x = -0.368394199 + 0.5

Combine like terms: -0.368394199 + 0.5 = 0.131605801
x = 0.131605801

Simplifying
x = 0.131605801

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.868394199, 0.131605801}
Solution
x = {0.868394199, 0.131605801}