t(t-3)=2(t-3)

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

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

Reorder the terms:
t(-3 + t) = 2(t + -3)
(-3 * t + t * t) = 2(t + -3)
(-3t + t2) = 2(t + -3)

Reorder the terms:
-3t + t2 = 2(-3 + t)
-3t + t2 = (-3 * 2 + t * 2)
-3t + t2 = (-6 + 2t)

Solving
-3t + t2 = -6 + 2t

Solving for variable 't'.

Reorder the terms:
6 + -3t + -2t + t2 = -6 + 2t + 6 + -2t

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

Reorder the terms:
6 + -5t + t2 = -6 + 6 + 2t + -2t

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

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

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}