(t-2)(t-5)=-2

Solution for (t-2)(t-5)=-2 equation:

Simplifying
(t + -2)(t + -5) = -2

Reorder the terms:
(-2 + t)(t + -5) = -2

Reorder the terms:
(-2 + t)(-5 + t) = -2

Multiply (-2 + t) * (-5 + t)
(-2(-5 + t) + t(-5 + t)) = -2
((-5 * -2 + t * -2) + t(-5 + t)) = -2
((10 + -2t) + t(-5 + t)) = -2
(10 + -2t + (-5 * t + t * t)) = -2
(10 + -2t + (-5t + t2)) = -2

Combine like terms: -2t + -5t = -7t
(10 + -7t + t2) = -2

Solving
10 + -7t + t2 = -2

Solving for variable 't'.

Reorder the terms:
10 + 2 + -7t + t2 = -2 + 2

Combine like terms: 10 + 2 = 12
12 + -7t + t2 = -2 + 2

Combine like terms: -2 + 2 = 0
12 + -7t + 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}