0=20y^2(y^3-y^2-40y+112)

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Solution for 0=20y^2(y^3-y^2-40y+112) equation: 


Simplifying
0 = 20y2(y3 + -1y2 + -40y + 112)

Reorder the terms:
0 = 20y2(112 + -40y + -1y2 + y3)
0 = (112 * 20y2 + -40y * 20y2 + -1y2 * 20y2 + y3 * 20y2)
0 = (2240y2 + -800y3 + -20y4 + 20y5)

Solving
0 = 2240y2 + -800y3 + -20y4 + 20y5

Solving for variable 'y'.
Remove the zero:
-2240y2 + 800y3 + 20y4 + -20y5 = 2240y2 + -800y3 + -20y4 + 20y5 + -2240y2 + 800y3 + 20y4 + -20y5

Reorder the terms:
-2240y2 + 800y3 + 20y4 + -20y5 = 2240y2 + -2240y2 + -800y3 + 800y3 + -20y4 + 20y4 + 20y5 + -20y5

Combine like terms: 2240y2 + -2240y2 = 0
-2240y2 + 800y3 + 20y4 + -20y5 = 0 + -800y3 + 800y3 + -20y4 + 20y4 + 20y5 + -20y5
-2240y2 + 800y3 + 20y4 + -20y5 = -800y3 + 800y3 + -20y4 + 20y4 + 20y5 + -20y5

Combine like terms: -800y3 + 800y3 = 0
-2240y2 + 800y3 + 20y4 + -20y5 = 0 + -20y4 + 20y4 + 20y5 + -20y5
-2240y2 + 800y3 + 20y4 + -20y5 = -20y4 + 20y4 + 20y5 + -20y5

Combine like terms: -20y4 + 20y4 = 0
-2240y2 + 800y3 + 20y4 + -20y5 = 0 + 20y5 + -20y5
-2240y2 + 800y3 + 20y4 + -20y5 = 20y5 + -20y5

Combine like terms: 20y5 + -20y5 = 0
-2240y2 + 800y3 + 20y4 + -20y5 = 0

Factor out the Greatest Common Factor (GCF), '20y2'.
20y2(-112 + 40y + y2 + -1y3) = 0

Ignore the factor 20.

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 '(-112 + 40y + y2 + -1y3)' equal to zero and attempt to solve:

Simplifying
-112 + 40y + y2 + -1y3 = 0

Solving
-112 + 40y + y2 + -1y3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}

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