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

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

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

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

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

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

Combine like terms: 3t + 7t = 10t
(21 + 10t + t2) = 0

Solving
21 + 10t + t2 = 0

Solving for variable 't'.

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

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

Simplifying
7 + t = 0

Solving
7 + t = 0

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

Add '-7' to each side of the equation.
7 + -7 + t = 0 + -7

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

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

Simplifying
t = -7
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 = {-7, -3}