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

Solution for (t+3)*(2t+6)= equation:

Simplifying
(t + 3)(2t + 6) = 0

Reorder the terms:
(3 + t)(2t + 6) = 0

Reorder the terms:
(3 + t)(6 + 2t) = 0

Multiply (3 + t) * (6 + 2t)
(3(6 + 2t) + t(6 + 2t)) = 0
((6 * 3 + 2t * 3) + t(6 + 2t)) = 0
((18 + 6t) + t(6 + 2t)) = 0
(18 + 6t + (6 * t + 2t * t)) = 0
(18 + 6t + (6t + 2t2)) = 0

Combine like terms: 6t + 6t = 12t
(18 + 12t + 2t2) = 0

Solving
18 + 12t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 6t + t2) = 0

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

Ignore the factor 2.
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 + 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
Solution
t = {-3, -3}