12y=3(3y^2+1)

Solution for 12y=3(3y^2+1) equation:

Simplifying
12y = 3(3y2 + 1)

Reorder the terms:
12y = 3(1 + 3y2)
12y = (1 * 3 + 3y2 * 3)
12y = (3 + 9y2)

Solving
12y = 3 + 9y2

Solving for variable 'y'.

Reorder the terms:
-3 + 12y + -9y2 = 3 + 9y2 + -3 + -9y2

Reorder the terms:
-3 + 12y + -9y2 = 3 + -3 + 9y2 + -9y2

Combine like terms: 3 + -3 = 0
-3 + 12y + -9y2 = 0 + 9y2 + -9y2
-3 + 12y + -9y2 = 9y2 + -9y2

Combine like terms: 9y2 + -9y2 = 0
-3 + 12y + -9y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 4y + -3y2) = 0

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

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

Simplifying
-1 + y = 0

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

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

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

Simplifying
y = 1
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, 0.3333333333}