6y^2-y=7

Solution for 6y^2-y=7 equation:

Simplifying
6y2 + -1y = 7

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

Solving
-1y + 6y2 = 7

Solving for variable 'y'.

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

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

Factor a trinomial.
(-1 + -1y)(7 + -6y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -6y)' equal to zero and attempt to solve:

Simplifying
7 + -6y = 0

Solving
7 + -6y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -6y = 0 + -7

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

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

Divide each side by '-6'.
y = 1.166666667

Simplifying
y = 1.166666667
Solution
y = {-1, 1.166666667}