(3t+5)(t+3)=7

Solution for (3t+5)(t+3)=7 equation:

Simplifying
(3t + 5)(t + 3) = 7

Reorder the terms:
(5 + 3t)(t + 3) = 7

Reorder the terms:
(5 + 3t)(3 + t) = 7

Multiply (5 + 3t) * (3 + t)
(5(3 + t) + 3t * (3 + t)) = 7
((3 * 5 + t * 5) + 3t * (3 + t)) = 7
((15 + 5t) + 3t * (3 + t)) = 7
(15 + 5t + (3 * 3t + t * 3t)) = 7
(15 + 5t + (9t + 3t2)) = 7

Combine like terms: 5t + 9t = 14t
(15 + 14t + 3t2) = 7

Solving
15 + 14t + 3t2 = 7

Solving for variable 't'.

Reorder the terms:
15 + -7 + 14t + 3t2 = 7 + -7

Combine like terms: 15 + -7 = 8
8 + 14t + 3t2 = 7 + -7

Combine like terms: 7 + -7 = 0
8 + 14t + 3t2 = 0

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

Subproblem 1
Set the factor '(4 + t)' equal to zero and attempt to solve:

Simplifying
4 + t = 0

Solving
4 + t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + t = 0 + -4
t = 0 + -4

Combine like terms: 0 + -4 = -4
t = -4

Simplifying
t = -4
Subproblem 2
Set the factor '(2 + 3t)' equal to zero and attempt to solve:

Simplifying
2 + 3t = 0

Solving
2 + 3t = 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 + 3t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3t = 0 + -2
3t = 0 + -2

Combine like terms: 0 + -2 = -2
3t = -2

Divide each side by '3'.
t = -0.6666666667

Simplifying
t = -0.6666666667
Solution
t = {-4, -0.6666666667}