(7t+2)(t+3)=0

Solution for (7t+2)(t+3)=0 equation:

Simplifying
(7t + 2)(t + 3) = 0

Reorder the terms:
(2 + 7t)(t + 3) = 0

Reorder the terms:
(2 + 7t)(3 + t) = 0

Multiply (2 + 7t) * (3 + t)
(2(3 + t) + 7t * (3 + t)) = 0
((3 * 2 + t * 2) + 7t * (3 + t)) = 0
((6 + 2t) + 7t * (3 + t)) = 0
(6 + 2t + (3 * 7t + t * 7t)) = 0
(6 + 2t + (21t + 7t2)) = 0

Combine like terms: 2t + 21t = 23t
(6 + 23t + 7t2) = 0

Solving
6 + 23t + 7t2 = 0

Solving for variable 't'.

Factor a trinomial.
(3 + t)(2 + 7t) = 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 + 7t)' equal to zero and attempt to solve:

Simplifying
2 + 7t = 0

Solving
2 + 7t = 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 + 7t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7t = 0 + -2
7t = 0 + -2

Combine like terms: 0 + -2 = -2
7t = -2

Divide each side by '7'.
t = -0.2857142857

Simplifying
t = -0.2857142857
Solution
t = {-3, -0.2857142857}