4u^2=4u-6

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

Simplifying
4u2 = 4u + -6

Reorder the terms:
4u2 = -6 + 4u

Solving
4u2 = -6 + 4u

Solving for variable 'u'.

Reorder the terms:
6 + -4u + 4u2 = -6 + 4u + 6 + -4u

Reorder the terms:
6 + -4u + 4u2 = -6 + 6 + 4u + -4u

Combine like terms: -6 + 6 = 0
6 + -4u + 4u2 = 0 + 4u + -4u
6 + -4u + 4u2 = 4u + -4u

Combine like terms: 4u + -4u = 0
6 + -4u + 4u2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -2u + 2u2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -2u + 2u2)' equal to zero and attempt to solve:

Simplifying
3 + -2u + 2u2 = 0

Solving
3 + -2u + 2u2 = 0

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

Divide each side by '2'.
1.5 + -1u + u2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -1u + -1.5 + u2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -1u + u2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -1u + u2 = 0 + -1.5
-1u + u2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-1u + u2 = -1.5

The u term is -1u.  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.
-1u + 0.25 + u2 = -1.5 + 0.25

Reorder the terms:
0.25 + -1u + u2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + -1u + u2 = -1.25

Factor a perfect square on the left side:
(u + -0.5)(u + -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.