8t^2+32t+14=0

Solution for 8t^2+32t+14=0 equation:

Simplifying
8t2 + 32t + 14 = 0

Reorder the terms:
14 + 32t + 8t2 = 0

Solving
14 + 32t + 8t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 16t + 4t2) = 0

Factor a trinomial.
2((7 + 2t)(1 + 2t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + 2t)' equal to zero and attempt to solve:

Simplifying
7 + 2t = 0

Solving
7 + 2t = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2t = 0 + -7
2t = 0 + -7

Combine like terms: 0 + -7 = -7
2t = -7

Divide each side by '2'.
t = -3.5

Simplifying
t = -3.5
Subproblem 2
Set the factor '(1 + 2t)' equal to zero and attempt to solve:

Simplifying
1 + 2t = 0

Solving
1 + 2t = 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 + 2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2t = 0 + -1
2t = 0 + -1

Combine like terms: 0 + -1 = -1
2t = -1

Divide each side by '2'.
t = -0.5

Simplifying
t = -0.5
Solution
t = {-3.5, -0.5}