(2t+5)(t+4)=0

Solution for (2t+5)(t+4)=0 equation:

Simplifying
(2t + 5)(t + 4) = 0

Reorder the terms:
(5 + 2t)(t + 4) = 0

Reorder the terms:
(5 + 2t)(4 + t) = 0

Multiply (5 + 2t) * (4 + t)
(5(4 + t) + 2t * (4 + t)) = 0
((4 * 5 + t * 5) + 2t * (4 + t)) = 0
((20 + 5t) + 2t * (4 + t)) = 0
(20 + 5t + (4 * 2t + t * 2t)) = 0
(20 + 5t + (8t + 2t2)) = 0

Combine like terms: 5t + 8t = 13t
(20 + 13t + 2t2) = 0

Solving
20 + 13t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(4 + t)(5 + 2t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + 2t)' equal to zero and attempt to solve:

Simplifying
5 + 2t = 0

Solving
5 + 2t = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2t = 0 + -5
2t = 0 + -5

Combine like terms: 0 + -5 = -5
2t = -5

Divide each side by '2'.
t = -2.5

Simplifying
t = -2.5
Solution
t = {-4, -2.5}