4y^4(2y+1)(y-6)=0

Solution for 4y^4(2y+1)(y-6)=0 equation:

Simplifying
4y4(2y + 1)(y + -6) = 0

Reorder the terms:
4y4(1 + 2y)(y + -6) = 0

Reorder the terms:
4y4(1 + 2y)(-6 + y) = 0

Multiply (1 + 2y) * (-6 + y)
4y4(1(-6 + y) + 2y * (-6 + y)) = 0
4y4((-6 * 1 + y * 1) + 2y * (-6 + y)) = 0
4y4((-6 + 1y) + 2y * (-6 + y)) = 0
4y4(-6 + 1y + (-6 * 2y + y * 2y)) = 0
4y4(-6 + 1y + (-12y + 2y2)) = 0

Combine like terms: 1y + -12y = -11y
4y4(-6 + -11y + 2y2) = 0
(-6 * 4y4 + -11y * 4y4 + 2y2 * 4y4) = 0
(-24y4 + -44y5 + 8y6) = 0

Solving
-24y4 + -44y5 + 8y6 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4y4'.
4y4(-6 + -11y + 2y2) = 0

Factor a trinomial.
4y4((-1 + -2y)(6 + -1y)) = 0

Ignore the factor 4.
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 '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {-0.5, 6}