=-2r^5(r^2-8r-2)

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Solution for =-2r^5(r^2-8r-2) equation: 


Simplifying
0 = -2r5(r2 + -8r + -2)

Reorder the terms:
0 = -2r5(-2 + -8r + r2)
0 = (-2 * -2r5 + -8r * -2r5 + r2 * -2r5)
0 = (4r5 + 16r6 + -2r7)

Solving
0 = 4r5 + 16r6 + -2r7

Solving for variable 'r'.
Remove the zero:
-4r5 + -16r6 + 2r7 = 4r5 + 16r6 + -2r7 + -4r5 + -16r6 + 2r7

Reorder the terms:
-4r5 + -16r6 + 2r7 = 4r5 + -4r5 + 16r6 + -16r6 + -2r7 + 2r7

Combine like terms: 4r5 + -4r5 = 0
-4r5 + -16r6 + 2r7 = 0 + 16r6 + -16r6 + -2r7 + 2r7
-4r5 + -16r6 + 2r7 = 16r6 + -16r6 + -2r7 + 2r7

Combine like terms: 16r6 + -16r6 = 0
-4r5 + -16r6 + 2r7 = 0 + -2r7 + 2r7
-4r5 + -16r6 + 2r7 = -2r7 + 2r7

Combine like terms: -2r7 + 2r7 = 0
-4r5 + -16r6 + 2r7 = 0

Factor out the Greatest Common Factor (GCF), '2r5'.
2r5(-2 + -8r + r2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'r5' equal to zero and attempt to solve:

Simplifying
r5 = 0

Solving
r5 = 0

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

Simplifying
r5 = 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 '(-2 + -8r + r2)' equal to zero and attempt to solve:

Simplifying
-2 + -8r + r2 = 0

Solving
-2 + -8r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -8r + 2 + r2 = 0 + 2

Reorder the terms:
-2 + 2 + -8r + r2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -8r + r2 = 0 + 2
-8r + r2 = 0 + 2

Combine like terms: 0 + 2 = 2
-8r + r2 = 2

The r term is -8r.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8r + 16 + r2 = 2 + 16

Reorder the terms:
16 + -8r + r2 = 2 + 16

Combine like terms: 2 + 16 = 18
16 + -8r + r2 = 18

Factor a perfect square on the left side:
(r + -4)(r + -4) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(r + -4) equal to 4.242640687 and -4.242640687.


Subproblem 1
r + -4 = 4.242640687

Simplifying
r + -4 = 4.242640687

Reorder the terms:
-4 + r = 4.242640687

Solving
-4 + r = 4.242640687

Solving for variable 'r'.

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

Add '4' to each side of the equation.
-4 + 4 + r = 4.242640687 + 4

Combine like terms: -4 + 4 = 0
0 + r = 4.242640687 + 4
r = 4.242640687 + 4

Combine like terms: 4.242640687 + 4 = 8.242640687
r = 8.242640687

Simplifying
r = 8.242640687


Subproblem 2
r + -4 = -4.242640687

Simplifying
r + -4 = -4.242640687

Reorder the terms:
-4 + r = -4.242640687

Solving
-4 + r = -4.242640687

Solving for variable 'r'.

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

Add '4' to each side of the equation.
-4 + 4 + r = -4.242640687 + 4

Combine like terms: -4 + 4 = 0
0 + r = -4.242640687 + 4
r = -4.242640687 + 4

Combine like terms: -4.242640687 + 4 = -0.242640687
r = -0.242640687

Simplifying
r = -0.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {8.242640687, -0.242640687}
Solution
r = {8.242640687, -0.242640687}

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