(-8t^2-8t)(1t+1)=0

Solution for (-8t^2-8t)(1t+1)=0 equation:

Simplifying
(-8t2 + -8t)(1t + 1) = 0

Reorder the terms:
(-8t + -8t2)(1t + 1) = 0

Reorder the terms:
(-8t + -8t2)(1 + 1t) = 0

Multiply (-8t + -8t2) * (1 + 1t)
(-8t * (1 + 1t) + -8t2 * (1 + 1t)) = 0
((1 * -8t + 1t * -8t) + -8t2 * (1 + 1t)) = 0
((-8t + -8t2) + -8t2 * (1 + 1t)) = 0
(-8t + -8t2 + (1 * -8t2 + 1t * -8t2)) = 0
(-8t + -8t2 + (-8t2 + -8t3)) = 0

Combine like terms: -8t2 + -8t2 = -16t2
(-8t + -16t2 + -8t3) = 0

Solving
-8t + -16t2 + -8t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '-8t'.
-8t(1 + 2t + t2) = 0

Factor a trinomial.
-8t((1 + t)(1 + t)) = 0

Ignore the factor -8.
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 '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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

Add '-1' to each side of the equation.
1 + -1 + t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0 + -1
t = 0 + -1

Combine like terms: 0 + -1 = -1
t = -1

Simplifying
t = -1
Subproblem 3
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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

Add '-1' to each side of the equation.
1 + -1 + t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0 + -1
t = 0 + -1

Combine like terms: 0 + -1 = -1
t = -1

Simplifying
t = -1
Solution
t = {0, -1, -1}