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

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

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

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

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

Reorder the terms for easier multiplication:
2 * 3(3 + t)(2 + t) = 0

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

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

Combine like terms: 3t + 2t = 5t
6(6 + 5t + t2) = 0
(6 * 6 + 5t * 6 + t2 * 6) = 0
(36 + 30t + 6t2) = 0

Solving
36 + 30t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + 5t + t2) = 0

Factor a trinomial.
6((3 + t)(2 + t)) = 0

Ignore the factor 6.
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}