(t-9)(t+49)=0

Solution for (t-9)(t+49)=0 equation:

Simplifying
(t + -9)(t + 49) = 0

Reorder the terms:
(-9 + t)(t + 49) = 0

Reorder the terms:
(-9 + t)(49 + t) = 0

Multiply (-9 + t) * (49 + t)
(-9(49 + t) + t(49 + t)) = 0
((49 * -9 + t * -9) + t(49 + t)) = 0
((-441 + -9t) + t(49 + t)) = 0
(-441 + -9t + (49 * t + t * t)) = 0
(-441 + -9t + (49t + t2)) = 0

Combine like terms: -9t + 49t = 40t
(-441 + 40t + t2) = 0

Solving
-441 + 40t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-49 + -1t)(9 + -1t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve:

Simplifying
9 + -1t = 0

Solving
9 + -1t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1t = 0 + -9
-1t = 0 + -9

Combine like terms: 0 + -9 = -9
-1t = -9

Divide each side by '-1'.
t = 9

Simplifying
t = 9
Solution
t = {-49, 9}