t*(t+10)+24=0

Solution for t*(t+10)+24=0 equation:

Simplifying
t(t + 10) + 24 = 0

Reorder the terms:
t(10 + t) + 24 = 0
(10 * t + t * t) + 24 = 0
(10t + t2) + 24 = 0

Reorder the terms:
24 + 10t + t2 = 0

Solving
24 + 10t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(6 + t)(4 + t) = 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 '(4 + t)' equal to zero and attempt to solve:

Simplifying
4 + t = 0

Solving
4 + t = 0

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

Add '-4' to each side of the equation.
4 + -4 + t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + t = 0 + -4
t = 0 + -4

Combine like terms: 0 + -4 = -4
t = -4

Simplifying
t = -4
Solution
t = {-6, -4}