4y^2+1=4y

Solution for 4y^2+1=4y equation:

Simplifying
4y2 + 1 = 4y

Reorder the terms:
1 + 4y2 = 4y

Solving
1 + 4y2 = 4y

Solving for variable 'y'.

Reorder the terms:
1 + -4y + 4y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
1 + -4y + 4y2 = 0

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

Subproblem 1
Set the factor '(1 + -2y)' equal to zero and attempt to solve:

Simplifying
1 + -2y = 0

Solving
1 + -2y = 0

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

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

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

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

Divide each side by '-2'.
y = 0.5

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

Simplifying
1 + -2y = 0

Solving
1 + -2y = 0

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

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

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

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

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Solution
y = {0.5, 0.5}