(2t+5)(t+7)=0

Solution for (2t+5)(t+7)=0 equation:

Simplifying
(2t + 5)(t + 7) = 0

Reorder the terms:
(5 + 2t)(t + 7) = 0

Reorder the terms:
(5 + 2t)(7 + t) = 0

Multiply (5 + 2t) * (7 + t)
(5(7 + t) + 2t * (7 + t)) = 0
((7 * 5 + t * 5) + 2t * (7 + t)) = 0
((35 + 5t) + 2t * (7 + t)) = 0
(35 + 5t + (7 * 2t + t * 2t)) = 0
(35 + 5t + (14t + 2t2)) = 0

Combine like terms: 5t + 14t = 19t
(35 + 19t + 2t2) = 0

Solving
35 + 19t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(7 + t)(5 + 2t) = 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 '(5 + 2t)' equal to zero and attempt to solve:

Simplifying
5 + 2t = 0

Solving
5 + 2t = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2t = 0 + -5

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

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

Divide each side by '2'.
t = -2.5

Simplifying
t = -2.5
Solution
t = {-7, -2.5}