(4d^2-4d+1)y=0

Solution for (4d^2-4d+1)y=0 equation:

Simplifying
(4d2 + -4d + 1) * y = 0

Reorder the terms:
(1 + -4d + 4d2) * y = 0

Reorder the terms for easier multiplication:
y(1 + -4d + 4d2) = 0
(1 * y + -4d * y + 4d2 * y) = 0

Reorder the terms:
(-4dy + 4d2y + 1y) = 0
(-4dy + 4d2y + 1y) = 0

Solving
-4dy + 4d2y + 1y = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-4d + 4d2 + 1) = 0

Factor a trinomial.
y((2d + -1)(2d + -1)) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

Move all terms containing d to the left, all other terms to the right.

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(2d + -1)' equal to zero and attempt to solve:

Simplifying
2d + -1 = 0

Reorder the terms:
-1 + 2d = 0

Solving
-1 + 2d = 0

Move all terms containing d to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + 2d = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2d = 0 + 1
2d = 0 + 1

Combine like terms: 0 + 1 = 1
2d = 1

Divide each side by '2'.
d = 0.5

Simplifying
d = 0.5
Subproblem 3
Set the factor '(2d + -1)' equal to zero and attempt to solve:

Simplifying
2d + -1 = 0

Reorder the terms:
-1 + 2d = 0

Solving
-1 + 2d = 0

Move all terms containing d to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + 2d = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2d = 0 + 1
2d = 0 + 1

Combine like terms: 0 + 1 = 1
2d = 1

Divide each side by '2'.
d = 0.5

Simplifying
d = 0.5
Solution
d = {0.5, 0.5}