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

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

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

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

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

Multiply (4 + 3t) * (2 + t)
(4(2 + t) + 3t * (2 + t)) = 0
((2 * 4 + t * 4) + 3t * (2 + t)) = 0
((8 + 4t) + 3t * (2 + t)) = 0
(8 + 4t + (2 * 3t + t * 3t)) = 0
(8 + 4t + (6t + 3t2)) = 0

Combine like terms: 4t + 6t = 10t
(8 + 10t + 3t2) = 0

Solving
8 + 10t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(2 + t)(4 + 3t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + 3t)' equal to zero and attempt to solve:

Simplifying
4 + 3t = 0

Solving
4 + 3t = 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 + 3t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3t = 0 + -4
3t = 0 + -4

Combine like terms: 0 + -4 = -4
3t = -4

Divide each side by '3'.
t = -1.333333333

Simplifying
t = -1.333333333
Solution
t = {-2, -1.333333333}