t^2+14t=-24

Solution for t^2+14t=-24 equation:

Simplifying
t2 + 14t = -24

Reorder the terms:
14t + t2 = -24

Solving
14t + t2 = -24

Solving for variable 't'.

Reorder the terms:
24 + 14t + t2 = -24 + 24

Combine like terms: -24 + 24 = 0
24 + 14t + t2 = 0

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

Subproblem 1
Set the factor '(12 + t)' equal to zero and attempt to solve:

Simplifying
12 + t = 0

Solving
12 + t = 0

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

Add '-12' to each side of the equation.
12 + -12 + t = 0 + -12

Combine like terms: 12 + -12 = 0
0 + t = 0 + -12
t = 0 + -12

Combine like terms: 0 + -12 = -12
t = -12

Simplifying
t = -12
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 = {-12, -2}