t(t+8)+5(t+6)=

Solution for t(t+8)+5(t+6)= equation:

Simplifying
t(t + 8) + 5(t + 6) = 0

Reorder the terms:
t(8 + t) + 5(t + 6) = 0
(8 * t + t * t) + 5(t + 6) = 0
(8t + t2) + 5(t + 6) = 0

Reorder the terms:
8t + t2 + 5(6 + t) = 0
8t + t2 + (6 * 5 + t * 5) = 0
8t + t2 + (30 + 5t) = 0

Reorder the terms:
30 + 8t + 5t + t2 = 0

Combine like terms: 8t + 5t = 13t
30 + 13t + t2 = 0

Solving
30 + 13t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(10 + t)(3 + t) = 0

Subproblem 1
Set the factor '(10 + t)' equal to zero and attempt to solve:

Simplifying
10 + t = 0

Solving
10 + t = 0

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

Add '-10' to each side of the equation.
10 + -10 + t = 0 + -10

Combine like terms: 10 + -10 = 0
0 + t = 0 + -10
t = 0 + -10

Combine like terms: 0 + -10 = -10
t = -10

Simplifying
t = -10
Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 0

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

Add '-3' to each side of the equation.
3 + -3 + t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + t = 0 + -3
t = 0 + -3

Combine like terms: 0 + -3 = -3
t = -3

Simplifying
t = -3
Solution
t = {-10, -3}