4x-12x^2=256

Solution for 4x-12x^2=256 equation:

Simplifying
4x + -12x2 = 256

Solving
4x + -12x2 = 256

Solving for variable 'x'.

Reorder the terms:
-256 + 4x + -12x2 = 256 + -256

Combine like terms: 256 + -256 = 0
-256 + 4x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-64 + x + -3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-64 + x + -3x2)' equal to zero and attempt to solve:

Simplifying
-64 + x + -3x2 = 0

Solving
-64 + x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
21.33333333 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-21.33333333' to each side of the equation.
21.33333333 + -0.3333333333x + -21.33333333 + x2 = 0 + -21.33333333

Reorder the terms:
21.33333333 + -21.33333333 + -0.3333333333x + x2 = 0 + -21.33333333

Combine like terms: 21.33333333 + -21.33333333 = 0.00000000
0.00000000 + -0.3333333333x + x2 = 0 + -21.33333333
-0.3333333333x + x2 = 0 + -21.33333333

Combine like terms: 0 + -21.33333333 = -21.33333333
-0.3333333333x + x2 = -21.33333333

The x term is x.  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.
-0.3333333333x + 0.25 + x2 = -21.33333333 + 0.25

Reorder the terms:
0.25 + -0.3333333333x + x2 = -21.33333333 + 0.25

Combine like terms: -21.33333333 + 0.25 = -21.08333333
0.25 + -0.3333333333x + x2 = -21.08333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -21.08333333

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.