(t+7)(t+4)=4

Solution for (t+7)(t+4)=4 equation:

Simplifying
(t + 7)(t + 4) = 4

Reorder the terms:
(7 + t)(t + 4) = 4

Reorder the terms:
(7 + t)(4 + t) = 4

Multiply (7 + t) * (4 + t)
(7(4 + t) + t(4 + t)) = 4
((4 * 7 + t * 7) + t(4 + t)) = 4
((28 + 7t) + t(4 + t)) = 4
(28 + 7t + (4 * t + t * t)) = 4
(28 + 7t + (4t + t2)) = 4

Combine like terms: 7t + 4t = 11t
(28 + 11t + t2) = 4

Solving
28 + 11t + t2 = 4

Solving for variable 't'.

Reorder the terms:
28 + -4 + 11t + t2 = 4 + -4

Combine like terms: 28 + -4 = 24
24 + 11t + t2 = 4 + -4

Combine like terms: 4 + -4 = 0
24 + 11t + t2 = 0

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

Subproblem 1
Set the factor '(8 + t)' equal to zero and attempt to solve:

Simplifying
8 + t = 0

Solving
8 + t = 0

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

Add '-8' to each side of the equation.
8 + -8 + t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + t = 0 + -8
t = 0 + -8

Combine like terms: 0 + -8 = -8
t = -8

Simplifying
t = -8
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 = {-8, -3}