3y^2-6=7y

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

Simplifying
3y2 + -6 = 7y

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

Solving
-6 + 3y2 = 7y

Solving for variable 'y'.

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
y = {-0.6666666667, 3}