4x^2=4x-6

Solution for 4x^2=4x-6 equation:

Simplifying
4x2 = 4x + -6

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

Solving
4x2 = -6 + 4x

Solving for variable 'x'.

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

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

Combine like terms: -6 + 6 = 0
6 + -4x + 4x2 = 0 + 4x + -4x
6 + -4x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
6 + -4x + 4x2 = 0

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

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

Simplifying
3 + -2x + 2x2 = 0

Solving
3 + -2x + 2x2 = 0

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

Divide each side by '2'.
1.5 + -1x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -1x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -1x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -1x + x2 = 0 + -1.5
-1x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-1x + x2 = -1.5

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 = -1.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + -1x + x2 = -1.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -1.25

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.