(t-12)(t-5)=

Solution for (t-12)(t-5)= equation:

Simplifying
(t + -12)(t + -5) = 0

Reorder the terms:
(-12 + t)(t + -5) = 0

Reorder the terms:
(-12 + t)(-5 + t) = 0

Multiply (-12 + t) * (-5 + t)
(-12(-5 + t) + t(-5 + t)) = 0
((-5 * -12 + t * -12) + t(-5 + t)) = 0
((60 + -12t) + t(-5 + t)) = 0
(60 + -12t + (-5 * t + t * t)) = 0
(60 + -12t + (-5t + t2)) = 0

Combine like terms: -12t + -5t = -17t
(60 + -17t + t2) = 0

Solving
60 + -17t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(5 + -1t)(12 + -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 '(12 + -1t)' equal to zero and attempt to solve:

Simplifying
12 + -1t = 0

Solving
12 + -1t = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1t = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1t = 0 + -12
-1t = 0 + -12

Combine like terms: 0 + -12 = -12
-1t = -12

Divide each side by '-1'.
t = 12

Simplifying
t = 12
Solution
t = {5, 12}