6y+1=16y^2

Solution for 6y+1=16y^2 equation:

Simplifying
6y + 1 = 16y2

Reorder the terms:
1 + 6y = 16y2

Solving
1 + 6y = 16y2

Solving for variable 'y'.

Combine like terms: 16y2 + -16y2 = 0
1 + 6y + -16y2 = 0

Factor a trinomial.
(1 + -2y)(1 + 8y) = 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 + 8y)' equal to zero and attempt to solve:

Simplifying
1 + 8y = 0

Solving
1 + 8y = 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 + 8y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8y = 0 + -1
8y = 0 + -1

Combine like terms: 0 + -1 = -1
8y = -1

Divide each side by '8'.
y = -0.125

Simplifying
y = -0.125
Solution
y = {0.5, -0.125}