(t-16)(t+9)=0

Solution for (t-16)(t+9)=0 equation:

Simplifying
(t + -16)(t + 9) = 0

Reorder the terms:
(-16 + t)(t + 9) = 0

Reorder the terms:
(-16 + t)(9 + t) = 0

Multiply (-16 + t) * (9 + t)
(-16(9 + t) + t(9 + t)) = 0
((9 * -16 + t * -16) + t(9 + t)) = 0
((-144 + -16t) + t(9 + t)) = 0
(-144 + -16t + (9 * t + t * t)) = 0
(-144 + -16t + (9t + t2)) = 0

Combine like terms: -16t + 9t = -7t
(-144 + -7t + t2) = 0

Solving
-144 + -7t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-9 + -1t)(16 + -1t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(16 + -1t)' equal to zero and attempt to solve:

Simplifying
16 + -1t = 0

Solving
16 + -1t = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1t = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1t = 0 + -16
-1t = 0 + -16

Combine like terms: 0 + -16 = -16
-1t = -16

Divide each side by '-1'.
t = 16

Simplifying
t = 16
Solution
t = {-9, 16}