6y^2=7y-2

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

Simplifying
6y2 = 7y + -2

Reorder the terms:
6y2 = -2 + 7y

Solving
6y2 = -2 + 7y

Solving for variable 'y'.

Reorder the terms:
2 + -7y + 6y2 = -2 + 7y + 2 + -7y

Reorder the terms:
2 + -7y + 6y2 = -2 + 2 + 7y + -7y

Combine like terms: -2 + 2 = 0
2 + -7y + 6y2 = 0 + 7y + -7y
2 + -7y + 6y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
2 + -7y + 6y2 = 0

Factor a trinomial.
(1 + -2y)(2 + -3y) = 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 '(2 + -3y)' equal to zero and attempt to solve:

Simplifying
2 + -3y = 0

Solving
2 + -3y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3y = 0 + -2
-3y = 0 + -2

Combine like terms: 0 + -2 = -2
-3y = -2

Divide each side by '-3'.
y = 0.6666666667

Simplifying
y = 0.6666666667
Solution
y = {0.5, 0.6666666667}