(t-2)(t-2)-16=0

Solution for (t-2)(t-2)-16=0 equation:

Simplifying
(t + -2)(t + -2) + -16 = 0

Reorder the terms:
(-2 + t)(t + -2) + -16 = 0

Reorder the terms:
(-2 + t)(-2 + t) + -16 = 0

Multiply (-2 + t) * (-2 + t)
(-2(-2 + t) + t(-2 + t)) + -16 = 0
((-2 * -2 + t * -2) + t(-2 + t)) + -16 = 0
((4 + -2t) + t(-2 + t)) + -16 = 0
(4 + -2t + (-2 * t + t * t)) + -16 = 0
(4 + -2t + (-2t + t2)) + -16 = 0

Combine like terms: -2t + -2t = -4t
(4 + -4t + t2) + -16 = 0

Reorder the terms:
4 + -16 + -4t + t2 = 0

Combine like terms: 4 + -16 = -12
-12 + -4t + t2 = 0

Solving
-12 + -4t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-2 + -1t)(6 + -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 '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1t = 0 + -6

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

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

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {-2, 6}