-7t^3-t^2-3(5t^3-3t)=

Solution for -7t^3-t^2-3(5t^3-3t)= equation:

Simplifying
-7t3 + -1t2 + -3(5t3 + -3t) = 0

Reorder the terms:
-7t3 + -1t2 + -3(-3t + 5t3) = 0
-7t3 + -1t2 + (-3t * -3 + 5t3 * -3) = 0
-7t3 + -1t2 + (9t + -15t3) = 0

Reorder the terms:
9t + -1t2 + -7t3 + -15t3 = 0

Combine like terms: -7t3 + -15t3 = -22t3
9t + -1t2 + -22t3 = 0

Solving
9t + -1t2 + -22t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(9 + -1t + -22t2) = 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 '(9 + -1t + -22t2)' equal to zero and attempt to solve:

Simplifying
9 + -1t + -22t2 = 0

Solving
9 + -1t + -22t2 = 0

Begin completing the square.  Divide all terms by
-22 the coefficient of the squared term: 

Divide each side by '-22'.
-0.4090909091 + 0.04545454545t + t2 = 0

Move the constant term to the right:

Add '0.4090909091' to each side of the equation.
-0.4090909091 + 0.04545454545t + 0.4090909091 + t2 = 0 + 0.4090909091

Reorder the terms:
-0.4090909091 + 0.4090909091 + 0.04545454545t + t2 = 0 + 0.4090909091

Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000
0.0000000000 + 0.04545454545t + t2 = 0 + 0.4090909091
0.04545454545t + t2 = 0 + 0.4090909091

Combine like terms: 0 + 0.4090909091 = 0.4090909091
0.04545454545t + t2 = 0.4090909091

The t term is 0.04545454545t.  Take half its coefficient (0.02272727273).
Square it (0.0005165289257) and add it to both sides.

Add '0.0005165289257' to each side of the equation.
0.04545454545t + 0.0005165289257 + t2 = 0.4090909091 + 0.0005165289257

Reorder the terms:
0.0005165289257 + 0.04545454545t + t2 = 0.4090909091 + 0.0005165289257

Combine like terms: 0.4090909091 + 0.0005165289257 = 0.4096074380257
0.0005165289257 + 0.04545454545t + t2 = 0.4096074380257

Factor a perfect square on the left side:
(t + 0.02272727273)(t + 0.02272727273) = 0.4096074380257

Calculate the square root of the right side: 0.640005811

Break this problem into two subproblems by setting 
(t + 0.02272727273) equal to 0.640005811 and -0.640005811.

Subproblem 1
t + 0.02272727273 = 0.640005811

Simplifying
t + 0.02272727273 = 0.640005811

Reorder the terms:
0.02272727273 + t = 0.640005811

Solving
0.02272727273 + t = 0.640005811

Solving for variable 't'.

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

Add '-0.02272727273' to each side of the equation.
0.02272727273 + -0.02272727273 + t = 0.640005811 + -0.02272727273

Combine like terms: 0.02272727273 + -0.02272727273 = 0.00000000000
0.00000000000 + t = 0.640005811 + -0.02272727273
t = 0.640005811 + -0.02272727273

Combine like terms: 0.640005811 + -0.02272727273 = 0.61727853827
t = 0.61727853827

Simplifying
t = 0.61727853827

Subproblem 2
t + 0.02272727273 = -0.640005811

Simplifying
t + 0.02272727273 = -0.640005811

Reorder the terms:
0.02272727273 + t = -0.640005811

Solving
0.02272727273 + t = -0.640005811

Solving for variable 't'.

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

Add '-0.02272727273' to each side of the equation.
0.02272727273 + -0.02272727273 + t = -0.640005811 + -0.02272727273

Combine like terms: 0.02272727273 + -0.02272727273 = 0.00000000000
0.00000000000 + t = -0.640005811 + -0.02272727273
t = -0.640005811 + -0.02272727273

Combine like terms: -0.640005811 + -0.02272727273 = -0.66273308373
t = -0.66273308373

Simplifying
t = -0.66273308373

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.61727853827, -0.66273308373}
Solution
t = {0, 0.61727853827, -0.66273308373}