(5t+7)(t+5)=23

Solution for (5t+7)(t+5)=23 equation:

Simplifying
(5t + 7)(t + 5) = 23

Reorder the terms:
(7 + 5t)(t + 5) = 23

Reorder the terms:
(7 + 5t)(5 + t) = 23

Multiply (7 + 5t) * (5 + t)
(7(5 + t) + 5t * (5 + t)) = 23
((5 * 7 + t * 7) + 5t * (5 + t)) = 23
((35 + 7t) + 5t * (5 + t)) = 23
(35 + 7t + (5 * 5t + t * 5t)) = 23
(35 + 7t + (25t + 5t2)) = 23

Combine like terms: 7t + 25t = 32t
(35 + 32t + 5t2) = 23

Solving
35 + 32t + 5t2 = 23

Solving for variable 't'.

Reorder the terms:
35 + -23 + 32t + 5t2 = 23 + -23

Combine like terms: 35 + -23 = 12
12 + 32t + 5t2 = 23 + -23

Combine like terms: 23 + -23 = 0
12 + 32t + 5t2 = 0

Factor a trinomial.
(6 + t)(2 + 5t) = 0

Subproblem 1
Set the factor '(6 + t)' equal to zero and attempt to solve:

Simplifying
6 + t = 0

Solving
6 + t = 0

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

Add '-6' to each side of the equation.
6 + -6 + t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + t = 0 + -6
t = 0 + -6

Combine like terms: 0 + -6 = -6
t = -6

Simplifying
t = -6
Subproblem 2
Set the factor '(2 + 5t)' equal to zero and attempt to solve:

Simplifying
2 + 5t = 0

Solving
2 + 5t = 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 + 5t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5t = 0 + -2
5t = 0 + -2

Combine like terms: 0 + -2 = -2
5t = -2

Divide each side by '5'.
t = -0.4

Simplifying
t = -0.4
Solution
t = {-6, -0.4}