2y(5y^3-6y^2+y)=

Solution for 2y(5y^3-6y^2+y)= equation:

Simplifying
2y(5y3 + -6y2 + y) = 0

Reorder the terms:
2y(y + -6y2 + 5y3) = 0
(y * 2y + -6y2 * 2y + 5y3 * 2y) = 0
(2y2 + -12y3 + 10y4) = 0

Solving
2y2 + -12y3 + 10y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y2'.
2y2(1 + -6y + 5y2) = 0

Factor a trinomial.
2y2((1 + -5y)(1 + -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 + -5y)' equal to zero and attempt to solve:

Simplifying
1 + -5y = 0

Solving
1 + -5y = 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 + -5y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5y = 0 + -1
-5y = 0 + -1

Combine like terms: 0 + -1 = -1
-5y = -1

Divide each side by '-5'.
y = 0.2

Simplifying
y = 0.2
Subproblem 3
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1
Solution
y = {0, 0.2, 1}