t^2+28t+75=0

Solution for t^2+28t+75=0 equation:

Simplifying
t2 + 28t + 75 = 0

Reorder the terms:
75 + 28t + t2 = 0

Solving
75 + 28t + t2 = 0

Solving for variable 't'.

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

Subproblem 1
Set the factor '(25 + t)' equal to zero and attempt to solve:

Simplifying
25 + t = 0

Solving
25 + t = 0

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

Add '-25' to each side of the equation.
25 + -25 + t = 0 + -25

Combine like terms: 25 + -25 = 0
0 + t = 0 + -25
t = 0 + -25

Combine like terms: 0 + -25 = -25
t = -25

Simplifying
t = -25
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 = {-25, -3}