y^2(y-9)(2y-1)=0

Solution for y^2(y-9)(2y-1)=0 equation:

Simplifying
y2(y + -9)(2y + -1) = 0

Reorder the terms:
y2(-9 + y)(2y + -1) = 0

Reorder the terms:
y2(-9 + y)(-1 + 2y) = 0

Multiply (-9 + y) * (-1 + 2y)
y2(-9(-1 + 2y) + y(-1 + 2y)) = 0
y2((-1 * -9 + 2y * -9) + y(-1 + 2y)) = 0
y2((9 + -18y) + y(-1 + 2y)) = 0
y2(9 + -18y + (-1 * y + 2y * y)) = 0
y2(9 + -18y + (-1y + 2y2)) = 0

Combine like terms: -18y + -1y = -19y
y2(9 + -19y + 2y2) = 0
(9 * y2 + -19y * y2 + 2y2 * y2) = 0
(9y2 + -19y3 + 2y4) = 0

Solving
9y2 + -19y3 + 2y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(9 + -19y + 2y2) = 0

Factor a trinomial.
y2((1 + -2y)(9 + -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 '(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 '(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
Solution
y = {0, 0.5, 9}