3t(3t)(3t)+10t(10t)+8t=0

Solution for 3t(3t)(3t)+10t(10t)+8t=0 equation:

Simplifying
3t(3t)(3t) + 10t(10t) + 8t = 0

Remove parenthesis around (3t)
3t * 3t(3t) + 10t(10t) + 8t = 0

Remove parenthesis around (3t)
3t * 3t * 3t + 10t(10t) + 8t = 0

Reorder the terms for easier multiplication:
3 * 3 * 3t * t * t + 10t(10t) + 8t = 0

Multiply 3 * 3
9 * 3t * t * t + 10t(10t) + 8t = 0

Multiply 9 * 3
27t * t * t + 10t(10t) + 8t = 0

Multiply t * t
27t2 * t + 10t(10t) + 8t = 0

Multiply t2 * t
27t3 + 10t(10t) + 8t = 0

Remove parenthesis around (10t)
27t3 + 10t * 10t + 8t = 0

Reorder the terms for easier multiplication:
27t3 + 10 * 10t * t + 8t = 0

Multiply 10 * 10
27t3 + 100t * t + 8t = 0

Multiply t * t
27t3 + 100t2 + 8t = 0

Reorder the terms:
8t + 100t2 + 27t3 = 0

Solving
8t + 100t2 + 27t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(8 + 100t + 27t2) = 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 + 100t + 27t2)' equal to zero and attempt to solve:

Simplifying
8 + 100t + 27t2 = 0

Solving
8 + 100t + 27t2 = 0

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

Divide each side by '27'.
0.2962962963 + 3.703703704t + t2 = 0

Move the constant term to the right:

Add '-0.2962962963' to each side of the equation.
0.2962962963 + 3.703703704t + -0.2962962963 + t2 = 0 + -0.2962962963

Reorder the terms:
0.2962962963 + -0.2962962963 + 3.703703704t + t2 = 0 + -0.2962962963

Combine like terms: 0.2962962963 + -0.2962962963 = 0.0000000000
0.0000000000 + 3.703703704t + t2 = 0 + -0.2962962963
3.703703704t + t2 = 0 + -0.2962962963

Combine like terms: 0 + -0.2962962963 = -0.2962962963
3.703703704t + t2 = -0.2962962963

The t term is 3.703703704t.  Take half its coefficient (1.851851852).
Square it (3.429355282) and add it to both sides.

Add '3.429355282' to each side of the equation.
3.703703704t + 3.429355282 + t2 = -0.2962962963 + 3.429355282

Reorder the terms:
3.429355282 + 3.703703704t + t2 = -0.2962962963 + 3.429355282

Combine like terms: -0.2962962963 + 3.429355282 = 3.1330589857
3.429355282 + 3.703703704t + t2 = 3.1330589857

Factor a perfect square on the left side:
(t + 1.851851852)(t + 1.851851852) = 3.1330589857

Calculate the square root of the right side: 1.770044911

Break this problem into two subproblems by setting 
(t + 1.851851852) equal to 1.770044911 and -1.770044911.

Subproblem 1
t + 1.851851852 = 1.770044911

Simplifying
t + 1.851851852 = 1.770044911

Reorder the terms:
1.851851852 + t = 1.770044911

Solving
1.851851852 + t = 1.770044911

Solving for variable 't'.

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

Add '-1.851851852' to each side of the equation.
1.851851852 + -1.851851852 + t = 1.770044911 + -1.851851852

Combine like terms: 1.851851852 + -1.851851852 = 0.000000000
0.000000000 + t = 1.770044911 + -1.851851852
t = 1.770044911 + -1.851851852

Combine like terms: 1.770044911 + -1.851851852 = -0.081806941
t = -0.081806941

Simplifying
t = -0.081806941

Subproblem 2
t + 1.851851852 = -1.770044911

Simplifying
t + 1.851851852 = -1.770044911

Reorder the terms:
1.851851852 + t = -1.770044911

Solving
1.851851852 + t = -1.770044911

Solving for variable 't'.

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

Add '-1.851851852' to each side of the equation.
1.851851852 + -1.851851852 + t = -1.770044911 + -1.851851852

Combine like terms: 1.851851852 + -1.851851852 = 0.000000000
0.000000000 + t = -1.770044911 + -1.851851852
t = -1.770044911 + -1.851851852

Combine like terms: -1.770044911 + -1.851851852 = -3.621896763
t = -3.621896763

Simplifying
t = -3.621896763

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.081806941, -3.621896763}
Solution
t = {0, -0.081806941, -3.621896763}