(3t+5)(t+2)=0

Solution for (3t+5)(t+2)=0 equation:

Simplifying
(3t + 5)(t + 2) = 0

Reorder the terms:
(5 + 3t)(t + 2) = 0

Reorder the terms:
(5 + 3t)(2 + t) = 0

Multiply (5 + 3t) * (2 + t)
(5(2 + t) + 3t * (2 + t)) = 0
((2 * 5 + t * 5) + 3t * (2 + t)) = 0
((10 + 5t) + 3t * (2 + t)) = 0
(10 + 5t + (2 * 3t + t * 3t)) = 0
(10 + 5t + (6t + 3t2)) = 0

Combine like terms: 5t + 6t = 11t
(10 + 11t + 3t2) = 0

Solving
10 + 11t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(2 + t)(5 + 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 '(5 + 3t)' equal to zero and attempt to solve:

Simplifying
5 + 3t = 0

Solving
5 + 3t = 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 + 3t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3t = 0 + -5
3t = 0 + -5

Combine like terms: 0 + -5 = -5
3t = -5

Divide each side by '3'.
t = -1.666666667

Simplifying
t = -1.666666667
Solution
t = {-2, -1.666666667}