0=2t^2+13t+6

Solution for 0=2t^2+13t+6 equation:

Simplifying
0 = 2t2 + 13t + 6

Reorder the terms:
0 = 6 + 13t + 2t2

Solving
0 = 6 + 13t + 2t2

Solving for variable 't'.

Combine like terms: 0 + -6 = -6
-6 + -13t + -2t2 = 6 + 13t + 2t2 + -6 + -13t + -2t2

Reorder the terms:
-6 + -13t + -2t2 = 6 + -6 + 13t + -13t + 2t2 + -2t2

Combine like terms: 6 + -6 = 0
-6 + -13t + -2t2 = 0 + 13t + -13t + 2t2 + -2t2
-6 + -13t + -2t2 = 13t + -13t + 2t2 + -2t2

Combine like terms: 13t + -13t = 0
-6 + -13t + -2t2 = 0 + 2t2 + -2t2
-6 + -13t + -2t2 = 2t2 + -2t2

Combine like terms: 2t2 + -2t2 = 0
-6 + -13t + -2t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 13t + 2t2) = 0

Factor a trinomial.
-1((6 + t)(1 + 2t)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + t)' equal to zero and attempt to solve:

Simplifying
6 + t = 0

Solving
6 + t = 0

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

Add '-6' to each side of the equation.
6 + -6 + t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + t = 0 + -6
t = 0 + -6

Combine like terms: 0 + -6 = -6
t = -6

Simplifying
t = -6
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 = {-6, -0.5}