y^7-24y^6-192y^5=0

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Solution for y^7-24y^6-192y^5=0 equation: 


Simplifying
y7 + -24y6 + -192y5 = 0

Reorder the terms:
-192y5 + -24y6 + y7 = 0

Solving
-192y5 + -24y6 + y7 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y5'.
y5(-192 + -24y + y2) = 0


Subproblem 1
Set the factor 'y5' equal to zero and attempt to solve:

Simplifying
y5 = 0

Solving
y5 = 0

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

Simplifying
y5 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-192 + -24y + y2)' equal to zero and attempt to solve:

Simplifying
-192 + -24y + y2 = 0

Solving
-192 + -24y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '192' to each side of the equation.
-192 + -24y + 192 + y2 = 0 + 192

Reorder the terms:
-192 + 192 + -24y + y2 = 0 + 192

Combine like terms: -192 + 192 = 0
0 + -24y + y2 = 0 + 192
-24y + y2 = 0 + 192

Combine like terms: 0 + 192 = 192
-24y + y2 = 192

The y term is -24y.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24y + 144 + y2 = 192 + 144

Reorder the terms:
144 + -24y + y2 = 192 + 144

Combine like terms: 192 + 144 = 336
144 + -24y + y2 = 336

Factor a perfect square on the left side:
(y + -12)(y + -12) = 336

Calculate the square root of the right side: 18.33030278

Break this problem into two subproblems by setting 
(y + -12) equal to 18.33030278 and -18.33030278.


Subproblem 1
y + -12 = 18.33030278

Simplifying
y + -12 = 18.33030278

Reorder the terms:
-12 + y = 18.33030278

Solving
-12 + y = 18.33030278

Solving for variable 'y'.

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

Add '12' to each side of the equation.
-12 + 12 + y = 18.33030278 + 12

Combine like terms: -12 + 12 = 0
0 + y = 18.33030278 + 12
y = 18.33030278 + 12

Combine like terms: 18.33030278 + 12 = 30.33030278
y = 30.33030278

Simplifying
y = 30.33030278


Subproblem 2
y + -12 = -18.33030278

Simplifying
y + -12 = -18.33030278

Reorder the terms:
-12 + y = -18.33030278

Solving
-12 + y = -18.33030278

Solving for variable 'y'.

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

Add '12' to each side of the equation.
-12 + 12 + y = -18.33030278 + 12

Combine like terms: -12 + 12 = 0
0 + y = -18.33030278 + 12
y = -18.33030278 + 12

Combine like terms: -18.33030278 + 12 = -6.33030278
y = -6.33030278

Simplifying
y = -6.33030278


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {30.33030278, -6.33030278}
Solution
y = {30.33030278, -6.33030278}

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