t^2+27t+126=0

Solution for t^2+27t+126=0 equation:

Simplifying
t2 + 27t + 126 = 0

Reorder the terms:
126 + 27t + t2 = 0

Solving
126 + 27t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(21 + t)(6 + t) = 0

Subproblem 1
Set the factor '(21 + t)' equal to zero and attempt to solve:

Simplifying
21 + t = 0

Solving
21 + t = 0

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

Add '-21' to each side of the equation.
21 + -21 + t = 0 + -21

Combine like terms: 21 + -21 = 0
0 + t = 0 + -21
t = 0 + -21

Combine like terms: 0 + -21 = -21
t = -21

Simplifying
t = -21
Subproblem 2
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
Solution
t = {-21, -6}