(t-25)(t+16)=0

Solution for (t-25)(t+16)=0 equation:

Simplifying
(t + -25)(t + 16) = 0

Reorder the terms:
(-25 + t)(t + 16) = 0

Reorder the terms:
(-25 + t)(16 + t) = 0

Multiply (-25 + t) * (16 + t)
(-25(16 + t) + t(16 + t)) = 0
((16 * -25 + t * -25) + t(16 + t)) = 0
((-400 + -25t) + t(16 + t)) = 0
(-400 + -25t + (16 * t + t * t)) = 0
(-400 + -25t + (16t + t2)) = 0

Combine like terms: -25t + 16t = -9t
(-400 + -9t + t2) = 0

Solving
-400 + -9t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-16 + -1t)(25 + -1t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(25 + -1t)' equal to zero and attempt to solve:

Simplifying
25 + -1t = 0

Solving
25 + -1t = 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 + -1t = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1t = 0 + -25
-1t = 0 + -25

Combine like terms: 0 + -25 = -25
-1t = -25

Divide each side by '-1'.
t = 25

Simplifying
t = 25
Solution
t = {-16, 25}