7y=3y^2-6

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

Simplifying
7y = 3y2 + -6

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

Solving
7y = -6 + 3y2

Solving for variable 'y'.

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

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

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

Combine like terms: 3y2 + -3y2 = 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}