(x-6)(x-6)-16=0

Solution for (x-6)(x-6)-16=0 equation:

Simplifying
(x + -6)(x + -6) + -16 = 0

Reorder the terms:
(-6 + x)(x + -6) + -16 = 0

Reorder the terms:
(-6 + x)(-6 + x) + -16 = 0

Multiply (-6 + x) * (-6 + x)
(-6(-6 + x) + x(-6 + x)) + -16 = 0
((-6 * -6 + x * -6) + x(-6 + x)) + -16 = 0
((36 + -6x) + x(-6 + x)) + -16 = 0
(36 + -6x + (-6 * x + x * x)) + -16 = 0
(36 + -6x + (-6x + x2)) + -16 = 0

Combine like terms: -6x + -6x = -12x
(36 + -12x + x2) + -16 = 0

Reorder the terms:
36 + -16 + -12x + x2 = 0

Combine like terms: 36 + -16 = 20
20 + -12x + x2 = 0

Solving
20 + -12x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {2, 10}