2t^2+7t+11=5-6t

Solution for 2t^2+7t+11=5-6t equation:

Simplifying
2t2 + 7t + 11 = 5 + -6t

Reorder the terms:
11 + 7t + 2t2 = 5 + -6t

Solving
11 + 7t + 2t2 = 5 + -6t

Solving for variable 't'.

Reorder the terms:
11 + -5 + 7t + 6t + 2t2 = 5 + -6t + -5 + 6t

Combine like terms: 11 + -5 = 6
6 + 7t + 6t + 2t2 = 5 + -6t + -5 + 6t

Combine like terms: 7t + 6t = 13t
6 + 13t + 2t2 = 5 + -6t + -5 + 6t

Reorder the terms:
6 + 13t + 2t2 = 5 + -5 + -6t + 6t

Combine like terms: 5 + -5 = 0
6 + 13t + 2t2 = 0 + -6t + 6t
6 + 13t + 2t2 = -6t + 6t

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

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

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}