(t+2)(t-3)=6

Solution for (t+2)(t-3)=6 equation:

Simplifying
(t + 2)(t + -3) = 6

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

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

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

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

Solving
-6 + -1t + t2 = 6

Solving for variable 't'.

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

Combine like terms: -6 + -6 = -12
-12 + -1t + t2 = 6 + -6

Combine like terms: 6 + -6 = 0
-12 + -1t + t2 = 0

Factor a trinomial.
(-3 + -1t)(4 + -1t) = 0

Subproblem 1
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
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 = {-3, 4}