0=16t^2+20t+6

Solution for 0=16t^2+20t+6 equation:

Simplifying
0 = 16t2 + 20t + 6

Reorder the terms:
0 = 6 + 20t + 16t2

Solving
0 = 6 + 20t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -6 = -6
-6 + -20t + -16t2 = 6 + 20t + 16t2 + -6 + -20t + -16t2

Reorder the terms:
-6 + -20t + -16t2 = 6 + -6 + 20t + -20t + 16t2 + -16t2

Combine like terms: 6 + -6 = 0
-6 + -20t + -16t2 = 0 + 20t + -20t + 16t2 + -16t2
-6 + -20t + -16t2 = 20t + -20t + 16t2 + -16t2

Combine like terms: 20t + -20t = 0
-6 + -20t + -16t2 = 0 + 16t2 + -16t2
-6 + -20t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-6 + -20t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 10t + 8t2) = 0

Factor a trinomial.
-2((3 + 4t)(1 + 2t)) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(3 + 4t)' equal to zero and attempt to solve:

Simplifying
3 + 4t = 0

Solving
3 + 4t = 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 + 4t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4t = 0 + -3
4t = 0 + -3

Combine like terms: 0 + -3 = -3
4t = -3

Divide each side by '4'.
t = -0.75

Simplifying
t = -0.75
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 = {-0.75, -0.5}