8y^3(7y^2-4y-1)=

Solution for 8y^3(7y^2-4y-1)= equation:

Simplifying
8y3(7y2 + -4y + -1) = 0

Reorder the terms:
8y3(-1 + -4y + 7y2) = 0
(-1 * 8y3 + -4y * 8y3 + 7y2 * 8y3) = 0
(-8y3 + -32y4 + 56y5) = 0

Solving
-8y3 + -32y4 + 56y5 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '8y3'.
8y3(-1 + -4y + 7y2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'y3' equal to zero and attempt to solve:

Simplifying
y3 = 0

Solving
y3 = 0

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

Simplifying
y3 = 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 '(-1 + -4y + 7y2)' equal to zero and attempt to solve:

Simplifying
-1 + -4y + 7y2 = 0

Solving
-1 + -4y + 7y2 = 0

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

Divide each side by '7'.
-0.1428571429 + -0.5714285714y + y2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + -0.5714285714y + 0.1428571429 + y2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + -0.5714285714y + y2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + -0.5714285714y + y2 = 0 + 0.1428571429
-0.5714285714y + y2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
-0.5714285714y + y2 = 0.1428571429

The y term is -0.5714285714y.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714y + 0.08163265305 + y2 = 0.1428571429 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714y + y2 = 0.1428571429 + 0.08163265305

Combine like terms: 0.1428571429 + 0.08163265305 = 0.22448979595
0.08163265305 + -0.5714285714y + y2 = 0.22448979595

Factor a perfect square on the left side:
(y + -0.2857142857)(y + -0.2857142857) = 0.22448979595

Calculate the square root of the right side: 0.473803542

Break this problem into two subproblems by setting 
(y + -0.2857142857) equal to 0.473803542 and -0.473803542.

Subproblem 1
y + -0.2857142857 = 0.473803542

Simplifying
y + -0.2857142857 = 0.473803542

Reorder the terms:
-0.2857142857 + y = 0.473803542

Solving
-0.2857142857 + y = 0.473803542

Solving for variable 'y'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + y = 0.473803542 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + y = 0.473803542 + 0.2857142857
y = 0.473803542 + 0.2857142857

Combine like terms: 0.473803542 + 0.2857142857 = 0.7595178277
y = 0.7595178277

Simplifying
y = 0.7595178277

Subproblem 2
y + -0.2857142857 = -0.473803542

Simplifying
y + -0.2857142857 = -0.473803542

Reorder the terms:
-0.2857142857 + y = -0.473803542

Solving
-0.2857142857 + y = -0.473803542

Solving for variable 'y'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + y = -0.473803542 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + y = -0.473803542 + 0.2857142857
y = -0.473803542 + 0.2857142857

Combine like terms: -0.473803542 + 0.2857142857 = -0.1880892563
y = -0.1880892563

Simplifying
y = -0.1880892563

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.7595178277, -0.1880892563}
Solution
y = {0.7595178277, -0.1880892563}