4y=4y^2+1

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

Simplifying
4y = 4y2 + 1

Reorder the terms:
4y = 1 + 4y2

Solving
4y = 1 + 4y2

Solving for variable 'y'.

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

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

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

Combine like terms: 4y2 + -4y2 = 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}