3y^2=-7y+6

Solution for 3y^2=-7y+6 equation:

Simplifying
3y2 = -7y + 6

Reorder the terms:
3y2 = 6 + -7y

Solving
3y2 = 6 + -7y

Solving for variable 'y'.

Reorder the terms:
-6 + 7y + 3y2 = 6 + -7y + -6 + 7y

Reorder the terms:
-6 + 7y + 3y2 = 6 + -6 + -7y + 7y

Combine like terms: 6 + -6 = 0
-6 + 7y + 3y2 = 0 + -7y + 7y
-6 + 7y + 3y2 = -7y + 7y

Combine like terms: -7y + 7y = 0
-6 + 7y + 3y2 = 0

Factor a trinomial.
(-3 + -1y)(2 + -3y) = 0

Subproblem 1
Set the factor '(-3 + -1y)' equal to zero and attempt to solve:

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3
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 = {-3, 0.6666666667}