3x(2x-1)+4=1

Solution for 3x(2x-1)+4=1 equation:

Simplifying
3x(2x + -1) + 4 = 1

Reorder the terms:
3x(-1 + 2x) + 4 = 1
(-1 * 3x + 2x * 3x) + 4 = 1
(-3x + 6x2) + 4 = 1

Reorder the terms:
4 + -3x + 6x2 = 1

Solving
4 + -3x + 6x2 = 1

Solving for variable 'x'.

Reorder the terms:
4 + -1 + -3x + 6x2 = 1 + -1

Combine like terms: 4 + -1 = 3
3 + -3x + 6x2 = 1 + -1

Combine like terms: 1 + -1 = 0
3 + -3x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -1x + 2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -1x + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + -1x + 2x2 = 0

Solving
1 + -1x + 2x2 = 0

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

Divide each side by '2'.
0.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -0.5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -0.5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -0.5x + x2 = 0 + -0.5
-0.5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-0.5x + x2 = -0.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -0.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -0.5 + 0.0625

Combine like terms: -0.5 + 0.0625 = -0.4375
0.0625 + -0.5x + x2 = -0.4375

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -0.4375

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.