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

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

Simplifying
(t + -5)(t + -5) = 2(5 + -1t)

Reorder the terms:
(-5 + t)(t + -5) = 2(5 + -1t)

Reorder the terms:
(-5 + t)(-5 + t) = 2(5 + -1t)

Multiply (-5 + t) * (-5 + t)
(-5(-5 + t) + t(-5 + t)) = 2(5 + -1t)
((-5 * -5 + t * -5) + t(-5 + t)) = 2(5 + -1t)
((25 + -5t) + t(-5 + t)) = 2(5 + -1t)
(25 + -5t + (-5 * t + t * t)) = 2(5 + -1t)
(25 + -5t + (-5t + t2)) = 2(5 + -1t)

Combine like terms: -5t + -5t = -10t
(25 + -10t + t2) = 2(5 + -1t)
25 + -10t + t2 = (5 * 2 + -1t * 2)
25 + -10t + t2 = (10 + -2t)

Solving
25 + -10t + t2 = 10 + -2t

Solving for variable 't'.

Reorder the terms:
25 + -10 + -10t + 2t + t2 = 10 + -2t + -10 + 2t

Combine like terms: 25 + -10 = 15
15 + -10t + 2t + t2 = 10 + -2t + -10 + 2t

Combine like terms: -10t + 2t = -8t
15 + -8t + t2 = 10 + -2t + -10 + 2t

Reorder the terms:
15 + -8t + t2 = 10 + -10 + -2t + 2t

Combine like terms: 10 + -10 = 0
15 + -8t + t2 = 0 + -2t + 2t
15 + -8t + t2 = -2t + 2t

Combine like terms: -2t + 2t = 0
15 + -8t + t2 = 0

Factor a trinomial.
(3 + -1t)(5 + -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 '(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
Solution
t = {3, 5}