0=y^3-5y^2-14y

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Solution for 0=y^3-5y^2-14y equation: 


Simplifying
0 = y3 + -5y2 + -14y

Reorder the terms:
0 = -14y + -5y2 + y3

Solving
0 = -14y + -5y2 + y3

Solving for variable 'y'.
Remove the zero:
14y + 5y2 + -1y3 = -14y + -5y2 + y3 + 14y + 5y2 + -1y3

Reorder the terms:
14y + 5y2 + -1y3 = -14y + 14y + -5y2 + 5y2 + y3 + -1y3

Combine like terms: -14y + 14y = 0
14y + 5y2 + -1y3 = 0 + -5y2 + 5y2 + y3 + -1y3
14y + 5y2 + -1y3 = -5y2 + 5y2 + y3 + -1y3

Combine like terms: -5y2 + 5y2 = 0
14y + 5y2 + -1y3 = 0 + y3 + -1y3
14y + 5y2 + -1y3 = y3 + -1y3

Combine like terms: y3 + -1y3 = 0
14y + 5y2 + -1y3 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(14 + 5y + -1y2) = 0

Factor a trinomial.
y((7 + -1y)(2 + y)) = 0


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 '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7

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, 7, -2}

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