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

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

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

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

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

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

Combine like terms: 2t + -3t = -1t
(-6 + -1t + t2) = t + 2

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

Solving
-6 + -1t + t2 = 2 + t

Solving for variable 't'.

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

Combine like terms: -6 + -2 = -8
-8 + -1t + -1t + t2 = 2 + t + -2 + -1t

Combine like terms: -1t + -1t = -2t
-8 + -2t + t2 = 2 + t + -2 + -1t

Reorder the terms:
-8 + -2t + t2 = 2 + -2 + t + -1t

Combine like terms: 2 + -2 = 0
-8 + -2t + t2 = 0 + t + -1t
-8 + -2t + t2 = t + -1t

Combine like terms: t + -1t = 0
-8 + -2t + t2 = 0

Factor a trinomial.
(-2 + -1t)(4 + -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 '(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 = {-2, 4}