4x(1-x)=14

Solution for 4x(1-x)=14 equation:

Simplifying
4x(1 + -1x) = 14
(1 * 4x + -1x * 4x) = 14
(4x + -4x2) = 14

Solving
4x + -4x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + 4x + -4x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 4x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 2x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + 2x + -2x2)' equal to zero and attempt to solve:

Simplifying
-7 + 2x + -2x2 = 0

Solving
-7 + 2x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
3.5 + -1x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -1x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -1x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -1x + x2 = 0 + -3.5
-1x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-1x + x2 = -3.5

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 = -3.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -3.5 + 0.25

Combine like terms: -3.5 + 0.25 = -3.25
0.25 + -1x + x2 = -3.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -3.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.