4(x(1-x))=1

Solution for 4(x(1-x))=1 equation:

Simplifying
4(x(1 + -1x)) = 1
4((1 * x + -1x * x)) = 1
4((1x + -1x2)) = 1
(1x * 4 + -1x2 * 4) = 1
(4x + -4x2) = 1

Solving
4x + -4x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 4x + -4x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 4x + -4x2 = 0

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

Subproblem 1
Set the factor '(-1 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2x = 0 + 1

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

Combine like terms: 0 + 1 = 1
2x = 1

Divide each side by '2'.
x = 0.5

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

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

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

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

Simplifying
x = 0.5
Solution
x = {0.5, 0.5}