0=3t^2-8t-3

Solution for 0=3t^2-8t-3 equation:

Simplifying
0 = 3t2 + -8t + -3

Reorder the terms:
0 = -3 + -8t + 3t2

Solving
0 = -3 + -8t + 3t2

Solving for variable 't'.

Combine like terms: 0 + 3 = 3
3 + 8t + -3t2 = -3 + -8t + 3t2 + 3 + 8t + -3t2

Reorder the terms:
3 + 8t + -3t2 = -3 + 3 + -8t + 8t + 3t2 + -3t2

Combine like terms: -3 + 3 = 0
3 + 8t + -3t2 = 0 + -8t + 8t + 3t2 + -3t2
3 + 8t + -3t2 = -8t + 8t + 3t2 + -3t2

Combine like terms: -8t + 8t = 0
3 + 8t + -3t2 = 0 + 3t2 + -3t2
3 + 8t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
3 + 8t + -3t2 = 0

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

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

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Subproblem 2
Set the factor '(1 + 3t)' equal to zero and attempt to solve:

Simplifying
1 + 3t = 0

Solving
1 + 3t = 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 + 3t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3t = 0 + -1
3t = 0 + -1

Combine like terms: 0 + -1 = -1
3t = -1

Divide each side by '3'.
t = -0.3333333333

Simplifying
t = -0.3333333333
Solution
t = {3, -0.3333333333}