2t^2+17t+26=0

Solution for 2t^2+17t+26=0 equation:

Simplifying
2t2 + 17t + 26 = 0

Reorder the terms:
26 + 17t + 2t2 = 0

Solving
26 + 17t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(13 + 2t)(2 + t) = 0

Subproblem 1
Set the factor '(13 + 2t)' equal to zero and attempt to solve:

Simplifying
13 + 2t = 0

Solving
13 + 2t = 0

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

Add '-13' to each side of the equation.
13 + -13 + 2t = 0 + -13

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

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

Divide each side by '2'.
t = -6.5

Simplifying
t = -6.5
Subproblem 2
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
Solution
t = {-6.5, -2}