6y^2+1=7y

Solution for 6y^2+1=7y equation:

Simplifying
6y2 + 1 = 7y

Reorder the terms:
1 + 6y2 = 7y

Solving
1 + 6y2 = 7y

Solving for variable 'y'.

Reorder the terms:
1 + -7y + 6y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
1 + -7y + 6y2 = 0

Factor a trinomial.
(1 + -6y)(1 + -1y) = 0

Subproblem 1
Set the factor '(1 + -6y)' equal to zero and attempt to solve:

Simplifying
1 + -6y = 0

Solving
1 + -6y = 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 + -6y = 0 + -1

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

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

Divide each side by '-6'.
y = 0.1666666667

Simplifying
y = 0.1666666667
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

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

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

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

Divide each side by '-1'.
y = 1

Simplifying
y = 1
Solution
y = {0.1666666667, 1}