(1t+3)(2t+3)=

Solution for (1t+3)(2t+3)= equation:

Simplifying
(1t + 3)(2t + 3) = 0

Reorder the terms:
(3 + 1t)(2t + 3) = 0

Reorder the terms:
(3 + 1t)(3 + 2t) = 0

Multiply (3 + 1t) * (3 + 2t)
(3(3 + 2t) + 1t * (3 + 2t)) = 0
((3 * 3 + 2t * 3) + 1t * (3 + 2t)) = 0
((9 + 6t) + 1t * (3 + 2t)) = 0
(9 + 6t + (3 * 1t + 2t * 1t)) = 0
(9 + 6t + (3t + 2t2)) = 0

Combine like terms: 6t + 3t = 9t
(9 + 9t + 2t2) = 0

Solving
9 + 9t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(3 + t)(3 + 2t) = 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 '(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 = {-3, -1.5}