(x-1)(x+1)=8x-17

Solution for (x-1)(x+1)=8x-17 equation:

Simplifying
(x + -1)(x + 1) = 8x + -17

Reorder the terms:
(-1 + x)(x + 1) = 8x + -17

Reorder the terms:
(-1 + x)(1 + x) = 8x + -17

Multiply (-1 + x) * (1 + x)
(-1(1 + x) + x(1 + x)) = 8x + -17
((1 * -1 + x * -1) + x(1 + x)) = 8x + -17
((-1 + -1x) + x(1 + x)) = 8x + -17
(-1 + -1x + (1 * x + x * x)) = 8x + -17
(-1 + -1x + (1x + x2)) = 8x + -17

Combine like terms: -1x + 1x = 0
(-1 + 0 + x2) = 8x + -17
(-1 + x2) = 8x + -17

Reorder the terms:
-1 + x2 = -17 + 8x

Solving
-1 + x2 = -17 + 8x

Solving for variable 'x'.

Reorder the terms:
-1 + 17 + -8x + x2 = -17 + 8x + 17 + -8x

Combine like terms: -1 + 17 = 16
16 + -8x + x2 = -17 + 8x + 17 + -8x

Reorder the terms:
16 + -8x + x2 = -17 + 17 + 8x + -8x

Combine like terms: -17 + 17 = 0
16 + -8x + x2 = 0 + 8x + -8x
16 + -8x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
16 + -8x + x2 = 0

Factor a trinomial.
(4 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {4, 4}