(t-2)(t-3)=

Solution for (t-2)(t-3)= equation:

Simplifying
(t + -2)(t + -3) = 0

Reorder the terms:
(-2 + t)(t + -3) = 0

Reorder the terms:
(-2 + t)(-3 + t) = 0

Multiply (-2 + t) * (-3 + t)
(-2(-3 + t) + t(-3 + t)) = 0
((-3 * -2 + t * -2) + t(-3 + t)) = 0
((6 + -2t) + t(-3 + t)) = 0
(6 + -2t + (-3 * t + t * t)) = 0
(6 + -2t + (-3t + t2)) = 0

Combine like terms: -2t + -3t = -5t
(6 + -5t + t2) = 0

Solving
6 + -5t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(2 + -1t)(3 + -1t) = 0

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

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