6y^2=-7y+3

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

Simplifying
6y2 = -7y + 3

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

Solving
6y2 = 3 + -7y

Solving for variable 'y'.

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

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

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

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

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

Subproblem 1
Set the factor '(-3 + -2y)' equal to zero and attempt to solve:

Simplifying
-3 + -2y = 0

Solving
-3 + -2y = 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 + -2y = 0 + 3

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

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

Divide each side by '-2'.
y = -1.5

Simplifying
y = -1.5
Subproblem 2
Set the factor '(1 + -3y)' equal to zero and attempt to solve:

Simplifying
1 + -3y = 0

Solving
1 + -3y = 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 + -3y = 0 + -1

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

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

Divide each side by '-3'.
y = 0.3333333333

Simplifying
y = 0.3333333333
Solution
y = {-1.5, 0.3333333333}