(x^2-16)=16x+1

Solution for (x^2-16)=16x+1 equation:

Simplifying
(x2 + -16) = 16x + 1

Reorder the terms:
(-16 + x2) = 16x + 1

Remove parenthesis around (-16 + x2)
-16 + x2 = 16x + 1

Reorder the terms:
-16 + x2 = 1 + 16x

Solving
-16 + x2 = 1 + 16x

Solving for variable 'x'.

Reorder the terms:
-16 + -1 + -16x + x2 = 1 + 16x + -1 + -16x

Combine like terms: -16 + -1 = -17
-17 + -16x + x2 = 1 + 16x + -1 + -16x

Reorder the terms:
-17 + -16x + x2 = 1 + -1 + 16x + -16x

Combine like terms: 1 + -1 = 0
-17 + -16x + x2 = 0 + 16x + -16x
-17 + -16x + x2 = 16x + -16x

Combine like terms: 16x + -16x = 0
-17 + -16x + x2 = 0

Factor a trinomial.
(-1 + -1x)(17 + -1x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {-1, 17}