(2t-4)(t+1)=(t-3)(t-2)

Solution for (2t-4)(t+1)=(t-3)(t-2) equation:

Simplifying
(2t + -4)(t + 1) = (t + -3)(t + -2)

Reorder the terms:
(-4 + 2t)(t + 1) = (t + -3)(t + -2)

Reorder the terms:
(-4 + 2t)(1 + t) = (t + -3)(t + -2)

Multiply (-4 + 2t) * (1 + t)
(-4(1 + t) + 2t * (1 + t)) = (t + -3)(t + -2)
((1 * -4 + t * -4) + 2t * (1 + t)) = (t + -3)(t + -2)
((-4 + -4t) + 2t * (1 + t)) = (t + -3)(t + -2)
(-4 + -4t + (1 * 2t + t * 2t)) = (t + -3)(t + -2)
(-4 + -4t + (2t + 2t2)) = (t + -3)(t + -2)

Combine like terms: -4t + 2t = -2t
(-4 + -2t + 2t2) = (t + -3)(t + -2)

Reorder the terms:
-4 + -2t + 2t2 = (-3 + t)(t + -2)

Reorder the terms:
-4 + -2t + 2t2 = (-3 + t)(-2 + t)

Multiply (-3 + t) * (-2 + t)
-4 + -2t + 2t2 = (-3(-2 + t) + t(-2 + t))
-4 + -2t + 2t2 = ((-2 * -3 + t * -3) + t(-2 + t))
-4 + -2t + 2t2 = ((6 + -3t) + t(-2 + t))
-4 + -2t + 2t2 = (6 + -3t + (-2 * t + t * t))
-4 + -2t + 2t2 = (6 + -3t + (-2t + t2))

Combine like terms: -3t + -2t = -5t
-4 + -2t + 2t2 = (6 + -5t + t2)

Solving
-4 + -2t + 2t2 = 6 + -5t + t2

Solving for variable 't'.

Reorder the terms:
-4 + -6 + -2t + 5t + 2t2 + -1t2 = 6 + -5t + t2 + -6 + 5t + -1t2

Combine like terms: -4 + -6 = -10
-10 + -2t + 5t + 2t2 + -1t2 = 6 + -5t + t2 + -6 + 5t + -1t2

Combine like terms: -2t + 5t = 3t
-10 + 3t + 2t2 + -1t2 = 6 + -5t + t2 + -6 + 5t + -1t2

Combine like terms: 2t2 + -1t2 = 1t2
-10 + 3t + 1t2 = 6 + -5t + t2 + -6 + 5t + -1t2

Reorder the terms:
-10 + 3t + 1t2 = 6 + -6 + -5t + 5t + t2 + -1t2

Combine like terms: 6 + -6 = 0
-10 + 3t + 1t2 = 0 + -5t + 5t + t2 + -1t2
-10 + 3t + 1t2 = -5t + 5t + t2 + -1t2

Combine like terms: -5t + 5t = 0
-10 + 3t + 1t2 = 0 + t2 + -1t2
-10 + 3t + 1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-10 + 3t + 1t2 = 0

Factor a trinomial.
(-5 + -1t)(2 + -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 '(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
Solution
t = {-5, 2}