(3y^2+2)+1=y+3

Solution for (3y^2+2)+1=y+3 equation:

Simplifying
(3y2 + 2) + 1 = y + 3

Reorder the terms:
(2 + 3y2) + 1 = y + 3

Remove parenthesis around (2 + 3y2)
2 + 3y2 + 1 = y + 3

Reorder the terms:
2 + 1 + 3y2 = y + 3

Combine like terms: 2 + 1 = 3
3 + 3y2 = y + 3

Reorder the terms:
3 + 3y2 = 3 + y

Add '-3' to each side of the equation.
3 + -3 + 3y2 = 3 + -3 + y

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

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

Solving
3y2 = y

Solving for variable 'y'.

Reorder the terms:
-1y + 3y2 = y + -1y

Combine like terms: y + -1y = 0
-1y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1 + 3y) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
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 = {0, 0.3333333333}