0=8t^2+24t+16

Solution for 0=8t^2+24t+16 equation:

Simplifying
0 = 8t2 + 24t + 16

Reorder the terms:
0 = 16 + 24t + 8t2

Solving
0 = 16 + 24t + 8t2

Solving for variable 't'.

Combine like terms: 0 + -16 = -16
-16 + -24t + -8t2 = 16 + 24t + 8t2 + -16 + -24t + -8t2

Reorder the terms:
-16 + -24t + -8t2 = 16 + -16 + 24t + -24t + 8t2 + -8t2

Combine like terms: 16 + -16 = 0
-16 + -24t + -8t2 = 0 + 24t + -24t + 8t2 + -8t2
-16 + -24t + -8t2 = 24t + -24t + 8t2 + -8t2

Combine like terms: 24t + -24t = 0
-16 + -24t + -8t2 = 0 + 8t2 + -8t2
-16 + -24t + -8t2 = 8t2 + -8t2

Combine like terms: 8t2 + -8t2 = 0
-16 + -24t + -8t2 = 0

Factor out the Greatest Common Factor (GCF), '-8'.
-8(2 + 3t + t2) = 0

Factor a trinomial.
-8((2 + t)(1 + t)) = 0

Ignore the factor -8.
Subproblem 1
Set the factor '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 0

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

Add '-2' to each side of the equation.
2 + -2 + t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + t = 0 + -2
t = 0 + -2

Combine like terms: 0 + -2 = -2
t = -2

Simplifying
t = -2
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 = {-2, -1}