=4y^3-12y^2-40y

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Solution for =4y^3-12y^2-40y equation: 


Simplifying
0 = 4y3 + -12y2 + -40y

Reorder the terms:
0 = -40y + -12y2 + 4y3

Solving
0 = -40y + -12y2 + 4y3

Solving for variable 'y'.
Remove the zero:
40y + 12y2 + -4y3 = -40y + -12y2 + 4y3 + 40y + 12y2 + -4y3

Reorder the terms:
40y + 12y2 + -4y3 = -40y + 40y + -12y2 + 12y2 + 4y3 + -4y3

Combine like terms: -40y + 40y = 0
40y + 12y2 + -4y3 = 0 + -12y2 + 12y2 + 4y3 + -4y3
40y + 12y2 + -4y3 = -12y2 + 12y2 + 4y3 + -4y3

Combine like terms: -12y2 + 12y2 = 0
40y + 12y2 + -4y3 = 0 + 4y3 + -4y3
40y + 12y2 + -4y3 = 4y3 + -4y3

Combine like terms: 4y3 + -4y3 = 0
40y + 12y2 + -4y3 = 0

Factor out the Greatest Common Factor (GCF), '4y'.
4y(10 + 3y + -1y2) = 0

Factor a trinomial.
4y((5 + -1y)(2 + y)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
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

Subproblem 3
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 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 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

Simplifying
y = -2
Solution
y = {0, 5, -2}

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