(t-5)(t-3)=

Solution for (t-5)(t-3)= equation:

Simplifying
(t + -5)(t + -3) = 0

Reorder the terms:
(-5 + t)(t + -3) = 0

Reorder the terms:
(-5 + t)(-3 + t) = 0

Multiply (-5 + t) * (-3 + t)
(-5(-3 + t) + t(-3 + t)) = 0
((-3 * -5 + t * -5) + t(-3 + t)) = 0
((15 + -5t) + t(-3 + t)) = 0
(15 + -5t + (-3 * t + t * t)) = 0
(15 + -5t + (-3t + t2)) = 0

Combine like terms: -5t + -3t = -8t
(15 + -8t + t2) = 0

Solving
15 + -8t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(3 + -1t)(5 + -1t) = 0

Subproblem 1
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Subproblem 2
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
Solution
t = {3, 5}