(2t+3)(t+4)=

Solution for (2t+3)(t+4)= equation:

Simplifying
(2t + 3)(t + 4) = 0

Reorder the terms:
(3 + 2t)(t + 4) = 0

Reorder the terms:
(3 + 2t)(4 + t) = 0

Multiply (3 + 2t) * (4 + t)
(3(4 + t) + 2t * (4 + t)) = 0
((4 * 3 + t * 3) + 2t * (4 + t)) = 0
((12 + 3t) + 2t * (4 + t)) = 0
(12 + 3t + (4 * 2t + t * 2t)) = 0
(12 + 3t + (8t + 2t2)) = 0

Combine like terms: 3t + 8t = 11t
(12 + 11t + 2t2) = 0

Solving
12 + 11t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(4 + t)(3 + 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 '(3 + 2t)' equal to zero and attempt to solve:

Simplifying
3 + 2t = 0

Solving
3 + 2t = 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 + 2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2t = 0 + -3
2t = 0 + -3

Combine like terms: 0 + -3 = -3
2t = -3

Divide each side by '2'.
t = -1.5

Simplifying
t = -1.5
Solution
t = {-4, -1.5}