(7t+21)(t+9)=0

Solution for (7t+21)(t+9)=0 equation:

Simplifying
(7t + 21)(t + 9) = 0

Reorder the terms:
(21 + 7t)(t + 9) = 0

Reorder the terms:
(21 + 7t)(9 + t) = 0

Multiply (21 + 7t) * (9 + t)
(21(9 + t) + 7t * (9 + t)) = 0
((9 * 21 + t * 21) + 7t * (9 + t)) = 0
((189 + 21t) + 7t * (9 + t)) = 0
(189 + 21t + (9 * 7t + t * 7t)) = 0
(189 + 21t + (63t + 7t2)) = 0

Combine like terms: 21t + 63t = 84t
(189 + 84t + 7t2) = 0

Solving
189 + 84t + 7t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '7'.
7(27 + 12t + t2) = 0

Factor a trinomial.
7((9 + t)(3 + t)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(9 + t)' equal to zero and attempt to solve:

Simplifying
9 + t = 0

Solving
9 + t = 0

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

Add '-9' to each side of the equation.
9 + -9 + t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + t = 0 + -9
t = 0 + -9

Combine like terms: 0 + -9 = -9
t = -9

Simplifying
t = -9
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 = {-9, -3}