y^4+6y^3=27y^2

Solution for y^4+6y^3=27y^2 equation:

Simplifying
y4 + 6y3 = 27y2

Reorder the terms:
6y3 + y4 = 27y2

Solving
6y3 + y4 = 27y2

Solving for variable 'y'.

Reorder the terms:
-27y2 + 6y3 + y4 = 27y2 + -27y2

Combine like terms: 27y2 + -27y2 = 0
-27y2 + 6y3 + y4 = 0

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(-27 + 6y + y2) = 0

Factor a trinomial.
y2((-9 + -1y)(3 + -1y)) = 0

Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}
Subproblem 2
Set the factor '(-9 + -1y)' equal to zero and attempt to solve:

Simplifying
-9 + -1y = 0

Solving
-9 + -1y = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1y = 0 + 9
-1y = 0 + 9

Combine like terms: 0 + 9 = 9
-1y = 9

Divide each side by '-1'.
y = -9

Simplifying
y = -9
Subproblem 3
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, -9, 3}