5t^2((2t^3)+(2t^2)-(3t))=

Solution for 5t^2((2t^3)+(2t^2)-(3t))= equation:

Simplifying
5t2((2t3) + (2t2) + -1(3t)) = 0

Remove parenthesis around (3t)
5t2((2t3) + (2t2) + -1 * 3t) = 0

Multiply -1 * 3
5t2((2t3) + (2t2) + -3t) = 0

Reorder the terms:
5t2(-3t + (2t2) + (2t3)) = 0
(-3t * 5t2 + (2t2) * 5t2 + (2t3) * 5t2) = 0
(-15t3 + 10t4 + 10t5) = 0

Solving
-15t3 + 10t4 + 10t5 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5t3'.
5t3(-3 + 2t + 2t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 't3' equal to zero and attempt to solve:

Simplifying
t3 = 0

Solving
t3 = 0

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

Simplifying
t3 = 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 '(-3 + 2t + 2t2)' equal to zero and attempt to solve:

Simplifying
-3 + 2t + 2t2 = 0

Solving
-3 + 2t + 2t2 = 0

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

Divide each side by '2'.
-1.5 + t + t2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + t + 1.5 + t2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + t + t2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t + t2 = 0 + 1.5
t + t2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
t + t2 = 1.5

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

Add '0.25' to each side of the equation.
 + 0.25 + t2 = 1.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + t2 = 1.5 + 0.25

Combine like terms: 1.5 + 0.25 = 1.75
1.25 + t2 = 1.75

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(t + 0.5) equal to 1.322875656 and -1.322875656.

Subproblem 1
t + 0.5 = 1.322875656

Simplifying
t + 0.5 = 1.322875656

Reorder the terms:
0.5 + t = 1.322875656

Solving
0.5 + t = 1.322875656

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 1.322875656 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 1.322875656 + -0.5
t = 1.322875656 + -0.5

Combine like terms: 1.322875656 + -0.5 = 0.822875656
t = 0.822875656

Simplifying
t = 0.822875656

Subproblem 2
t + 0.5 = -1.322875656

Simplifying
t + 0.5 = -1.322875656

Reorder the terms:
0.5 + t = -1.322875656

Solving
0.5 + t = -1.322875656

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -1.322875656 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -1.322875656 + -0.5
t = -1.322875656 + -0.5

Combine like terms: -1.322875656 + -0.5 = -1.822875656
t = -1.822875656

Simplifying
t = -1.822875656

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.822875656, -1.822875656}
Solution
t = {0.822875656, -1.822875656}