y^4+4y^3=5y^2

Solution for y^4+4y^3=5y^2 equation:

Simplifying
y4 + 4y3 = 5y2

Reorder the terms:
4y3 + y4 = 5y2

Solving
4y3 + y4 = 5y2

Solving for variable 'y'.

Reorder the terms:
-5y2 + 4y3 + y4 = 5y2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
-5y2 + 4y3 + y4 = 0

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(-5 + 4y + y2) = 0

Factor a trinomial.
y2((-5 + -1y)(1 + -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 '(-5 + -1y)' equal to zero and attempt to solve:

Simplifying
-5 + -1y = 0

Solving
-5 + -1y = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1y = 0 + 5
-1y = 0 + 5

Combine like terms: 0 + 5 = 5
-1y = 5

Divide each side by '-1'.
y = -5

Simplifying
y = -5
Subproblem 3
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1
Solution
y = {0, -5, 1}