2y^4(2y+1)(y-2)=0

Solution for 2y^4(2y+1)(y-2)=0 equation:

Simplifying
2y4(2y + 1)(y + -2) = 0

Reorder the terms:
2y4(1 + 2y)(y + -2) = 0

Reorder the terms:
2y4(1 + 2y)(-2 + y) = 0

Multiply (1 + 2y) * (-2 + y)
2y4(1(-2 + y) + 2y * (-2 + y)) = 0
2y4((-2 * 1 + y * 1) + 2y * (-2 + y)) = 0
2y4((-2 + 1y) + 2y * (-2 + y)) = 0
2y4(-2 + 1y + (-2 * 2y + y * 2y)) = 0
2y4(-2 + 1y + (-4y + 2y2)) = 0

Combine like terms: 1y + -4y = -3y
2y4(-2 + -3y + 2y2) = 0
(-2 * 2y4 + -3y * 2y4 + 2y2 * 2y4) = 0
(-4y4 + -6y5 + 4y6) = 0

Solving
-4y4 + -6y5 + 4y6 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y4'.
2y4(-2 + -3y + 2y2) = 0

Factor a trinomial.
2y4((-1 + -2y)(2 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'y4' equal to zero and attempt to solve:

Simplifying
y4 = 0

Solving
y4 = 0

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

Simplifying
y4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
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 = {-0.5, 2}