5t^3-t^2-8t=0

Solution for 5t^3-t^2-8t=0 equation:

Simplifying
5t3 + -1t2 + -8t = 0

Reorder the terms:
-8t + -1t2 + 5t3 = 0

Solving
-8t + -1t2 + 5t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-8 + -1t + 5t2) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(-8 + -1t + 5t2)' equal to zero and attempt to solve:

Simplifying
-8 + -1t + 5t2 = 0

Solving
-8 + -1t + 5t2 = 0

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

Divide each side by '5'.
-1.6 + -0.2t + t2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -0.2t + 1.6 + t2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -0.2t + t2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -0.2t + t2 = 0 + 1.6
-0.2t + t2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-0.2t + t2 = 1.6

The t term is -0.2t.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2t + 0.01 + t2 = 1.6 + 0.01

Reorder the terms:
0.01 + -0.2t + t2 = 1.6 + 0.01

Combine like terms: 1.6 + 0.01 = 1.61
0.01 + -0.2t + t2 = 1.61

Factor a perfect square on the left side:
(t + -0.1)(t + -0.1) = 1.61

Calculate the square root of the right side: 1.268857754

Break this problem into two subproblems by setting 
(t + -0.1) equal to 1.268857754 and -1.268857754.

Subproblem 1
t + -0.1 = 1.268857754

Simplifying
t + -0.1 = 1.268857754

Reorder the terms:
-0.1 + t = 1.268857754

Solving
-0.1 + t = 1.268857754

Solving for variable 't'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + t = 1.268857754 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + t = 1.268857754 + 0.1
t = 1.268857754 + 0.1

Combine like terms: 1.268857754 + 0.1 = 1.368857754
t = 1.368857754

Simplifying
t = 1.368857754

Subproblem 2
t + -0.1 = -1.268857754

Simplifying
t + -0.1 = -1.268857754

Reorder the terms:
-0.1 + t = -1.268857754

Solving
-0.1 + t = -1.268857754

Solving for variable 't'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + t = -1.268857754 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + t = -1.268857754 + 0.1
t = -1.268857754 + 0.1

Combine like terms: -1.268857754 + 0.1 = -1.168857754
t = -1.168857754

Simplifying
t = -1.168857754

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.368857754, -1.168857754}
Solution
t = {0, 1.368857754, -1.168857754}