y^2(4y^2-18y-10)=0

Solution for y^2(4y^2-18y-10)=0 equation:

Simplifying
y2(4y2 + -18y + -10) = 0

Reorder the terms:
y2(-10 + -18y + 4y2) = 0
(-10 * y2 + -18y * y2 + 4y2 * y2) = 0
(-10y2 + -18y3 + 4y4) = 0

Solving
-10y2 + -18y3 + 4y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y2'.
2y2(-5 + -9y + 2y2) = 0

Factor a trinomial.
2y2((-1 + -2y)(5 + -1y)) = 0

Ignore the factor 2.
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 '(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
Solution
y = {0, -0.5, 5}