8r^4(6r^2-3r-5)=

Solution for 8r^4(6r^2-3r-5)= equation:

Simplifying
8r4(6r2 + -3r + -5) = 0

Reorder the terms:
8r4(-5 + -3r + 6r2) = 0
(-5 * 8r4 + -3r * 8r4 + 6r2 * 8r4) = 0
(-40r4 + -24r5 + 48r6) = 0

Solving
-40r4 + -24r5 + 48r6 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '8r4'.
8r4(-5 + -3r + 6r2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'r4' equal to zero and attempt to solve:

Simplifying
r4 = 0

Solving
r4 = 0

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

Simplifying
r4 = 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 '(-5 + -3r + 6r2)' equal to zero and attempt to solve:

Simplifying
-5 + -3r + 6r2 = 0

Solving
-5 + -3r + 6r2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-0.8333333333 + -0.5r + r2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -0.5r + 0.8333333333 + r2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -0.5r + r2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -0.5r + r2 = 0 + 0.8333333333
-0.5r + r2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-0.5r + r2 = 0.8333333333

The r term is -0.5r.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5r + 0.0625 + r2 = 0.8333333333 + 0.0625

Reorder the terms:
0.0625 + -0.5r + r2 = 0.8333333333 + 0.0625

Combine like terms: 0.8333333333 + 0.0625 = 0.8958333333
0.0625 + -0.5r + r2 = 0.8958333333

Factor a perfect square on the left side:
(r + -0.25)(r + -0.25) = 0.8958333333

Calculate the square root of the right side: 0.946484724

Break this problem into two subproblems by setting 
(r + -0.25) equal to 0.946484724 and -0.946484724.

Subproblem 1
r + -0.25 = 0.946484724

Simplifying
r + -0.25 = 0.946484724

Reorder the terms:
-0.25 + r = 0.946484724

Solving
-0.25 + r = 0.946484724

Solving for variable 'r'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + r = 0.946484724 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + r = 0.946484724 + 0.25
r = 0.946484724 + 0.25

Combine like terms: 0.946484724 + 0.25 = 1.196484724
r = 1.196484724

Simplifying
r = 1.196484724

Subproblem 2
r + -0.25 = -0.946484724

Simplifying
r + -0.25 = -0.946484724

Reorder the terms:
-0.25 + r = -0.946484724

Solving
-0.25 + r = -0.946484724

Solving for variable 'r'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + r = -0.946484724 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + r = -0.946484724 + 0.25
r = -0.946484724 + 0.25

Combine like terms: -0.946484724 + 0.25 = -0.696484724
r = -0.696484724

Simplifying
r = -0.696484724

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.196484724, -0.696484724}
Solution
r = {1.196484724, -0.696484724}