(T-2)(T-1)=6

Solution for (T-2)(T-1)=6 equation:

Simplifying
(T + -2)(T + -1) = 6

Reorder the terms:
(-2 + T)(T + -1) = 6

Reorder the terms:
(-2 + T)(-1 + T) = 6

Multiply (-2 + T) * (-1 + T)
(-2(-1 + T) + T(-1 + T)) = 6
((-1 * -2 + T * -2) + T(-1 + T)) = 6
((2 + -2T) + T(-1 + T)) = 6
(2 + -2T + (-1 * T + T * T)) = 6
(2 + -2T + (-1T + T2)) = 6

Combine like terms: -2T + -1T = -3T
(2 + -3T + T2) = 6

Solving
2 + -3T + T2 = 6

Solving for variable 'T'.

Reorder the terms:
2 + -6 + -3T + T2 = 6 + -6

Combine like terms: 2 + -6 = -4
-4 + -3T + T2 = 6 + -6

Combine like terms: 6 + -6 = 0
-4 + -3T + T2 = 0

Factor a trinomial.
(-1 + -1T)(4 + -1T) = 0

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

Simplifying
-1 + -1T = 0

Solving
-1 + -1T = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -1T = 0 + 1
-1T = 0 + 1

Combine like terms: 0 + 1 = 1
-1T = 1

Divide each side by '-1'.
T = -1

Simplifying
T = -1
Subproblem 2
Set the factor '(4 + -1T)' equal to zero and attempt to solve:

Simplifying
4 + -1T = 0

Solving
4 + -1T = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1T = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1T = 0 + -4
-1T = 0 + -4

Combine like terms: 0 + -4 = -4
-1T = -4

Divide each side by '-1'.
T = 4

Simplifying
T = 4
Solution
T = {-1, 4}