(t+5)(t-9)=0

Solution for (t+5)(t-9)=0 equation:

Simplifying
(t + 5)(t + -9) = 0

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

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

Multiply (5 + t) * (-9 + t)
(5(-9 + t) + t(-9 + t)) = 0
((-9 * 5 + t * 5) + t(-9 + t)) = 0
((-45 + 5t) + t(-9 + t)) = 0
(-45 + 5t + (-9 * t + t * t)) = 0
(-45 + 5t + (-9t + t2)) = 0

Combine like terms: 5t + -9t = -4t
(-45 + -4t + t2) = 0

Solving
-45 + -4t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-5 + -1t)(9 + -1t) = 0

Subproblem 1
Set the factor '(-5 + -1t)' equal to zero and attempt to solve:

Simplifying
-5 + -1t = 0

Solving
-5 + -1t = 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 + -1t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1t = 0 + 5
-1t = 0 + 5

Combine like terms: 0 + 5 = 5
-1t = 5

Divide each side by '-1'.
t = -5

Simplifying
t = -5
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 = {-5, 9}