12y+7y^3=33y

Solution for 12y+7y^3=33y equation:

Simplifying
12y + 7y3 = 33y

Solving
12y + 7y3 = 33y

Solving for variable 'y'.

Reorder the terms:
12y + -33y + 7y3 = 33y + -33y

Combine like terms: 12y + -33y = -21y
-21y + 7y3 = 33y + -33y

Combine like terms: 33y + -33y = 0
-21y + 7y3 = 0

Factor out the Greatest Common Factor (GCF), '7y'.
7y(-3 + y2) = 0

Ignore the factor 7.
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 '(-3 + y2)' equal to zero and attempt to solve:

Simplifying
-3 + y2 = 0

Solving
-3 + y2 = 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 + y2 = 0 + 3

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

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

Simplifying
y2 = 3

Take the square root of each side:
y = {-1.732050808, 1.732050808}
Solution
y = {0, -1.732050808, 1.732050808}