(t+6)(t+7)=30

Solution for (t+6)(t+7)=30 equation:

Simplifying
(t + 6)(t + 7) = 30

Reorder the terms:
(6 + t)(t + 7) = 30

Reorder the terms:
(6 + t)(7 + t) = 30

Multiply (6 + t) * (7 + t)
(6(7 + t) + t(7 + t)) = 30
((7 * 6 + t * 6) + t(7 + t)) = 30
((42 + 6t) + t(7 + t)) = 30
(42 + 6t + (7 * t + t * t)) = 30
(42 + 6t + (7t + t2)) = 30

Combine like terms: 6t + 7t = 13t
(42 + 13t + t2) = 30

Solving
42 + 13t + t2 = 30

Solving for variable 't'.

Reorder the terms:
42 + -30 + 13t + t2 = 30 + -30

Combine like terms: 42 + -30 = 12
12 + 13t + t2 = 30 + -30

Combine like terms: 30 + -30 = 0
12 + 13t + t2 = 0

Factor a trinomial.
(12 + t)(1 + t) = 0

Subproblem 1
Set the factor '(12 + t)' equal to zero and attempt to solve:

Simplifying
12 + t = 0

Solving
12 + t = 0

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

Add '-12' to each side of the equation.
12 + -12 + t = 0 + -12

Combine like terms: 12 + -12 = 0
0 + t = 0 + -12
t = 0 + -12

Combine like terms: 0 + -12 = -12
t = -12

Simplifying
t = -12
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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

Add '-1' to each side of the equation.
1 + -1 + t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0 + -1
t = 0 + -1

Combine like terms: 0 + -1 = -1
t = -1

Simplifying
t = -1
Solution
t = {-12, -1}