(t+2)(t-49)=0

Solution for (t+2)(t-49)=0 equation:

Simplifying
(t + 2)(t + -49) = 0

Reorder the terms:
(2 + t)(t + -49) = 0

Reorder the terms:
(2 + t)(-49 + t) = 0

Multiply (2 + t) * (-49 + t)
(2(-49 + t) + t(-49 + t)) = 0
((-49 * 2 + t * 2) + t(-49 + t)) = 0
((-98 + 2t) + t(-49 + t)) = 0
(-98 + 2t + (-49 * t + t * t)) = 0
(-98 + 2t + (-49t + t2)) = 0

Combine like terms: 2t + -49t = -47t
(-98 + -47t + t2) = 0

Solving
-98 + -47t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-2 + -1t)(49 + -1t) = 0

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

Simplifying
-2 + -1t = 0

Solving
-2 + -1t = 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 + -1t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1t = 0 + 2
-1t = 0 + 2

Combine like terms: 0 + 2 = 2
-1t = 2

Divide each side by '-1'.
t = -2

Simplifying
t = -2
Subproblem 2
Set the factor '(49 + -1t)' equal to zero and attempt to solve:

Simplifying
49 + -1t = 0

Solving
49 + -1t = 0

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

Add '-49' to each side of the equation.
49 + -49 + -1t = 0 + -49

Combine like terms: 49 + -49 = 0
0 + -1t = 0 + -49
-1t = 0 + -49

Combine like terms: 0 + -49 = -49
-1t = -49

Divide each side by '-1'.
t = 49

Simplifying
t = 49
Solution
t = {-2, 49}