(t+3)(t+2)=

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

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

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

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

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

Combine like terms: 3t + 2t = 5t
(6 + 5t + t2) = 0

Solving
6 + 5t + t2 = 0

Solving for variable 't'.

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

Subproblem 1
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
Subproblem 2
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
Solution
t = {-3, -2}