8t^2+32t+24=0

Solution for 8t^2+32t+24=0 equation:

Simplifying
8t2 + 32t + 24 = 0

Reorder the terms:
24 + 32t + 8t2 = 0

Solving
24 + 32t + 8t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(3 + 4t + t2) = 0

Factor a trinomial.
8((3 + t)(1 + t)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 0

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

Add '-3' to each side of the equation.
3 + -3 + t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + t = 0 + -3
t = 0 + -3

Combine like terms: 0 + -3 = -3
t = -3

Simplifying
t = -3
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
Solution
t = {-3, -1}