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

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

Simplifying
2y3 + 2y = 5y2

Reorder the terms:
2y + 2y3 = 5y2

Solving
2y + 2y3 = 5y2

Solving for variable 'y'.

Reorder the terms:
2y + -5y2 + 2y3 = 5y2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
2y + -5y2 + 2y3 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(2 + -5y + 2y2) = 0

Factor a trinomial.
y((1 + -2y)(2 + -1y)) = 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 + -2y)' equal to zero and attempt to solve:

Simplifying
1 + -2y = 0

Solving
1 + -2y = 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 + -2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2y = 0 + -1
-2y = 0 + -1

Combine like terms: 0 + -1 = -1
-2y = -1

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Subproblem 3
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {0, 0.5, 2}