(x-3)(x+3)-8x=0

Solution for (x-3)(x+3)-8x=0 equation:

Simplifying
(x + -3)(x + 3) + -8x = 0

Reorder the terms:
(-3 + x)(x + 3) + -8x = 0

Reorder the terms:
(-3 + x)(3 + x) + -8x = 0

Multiply (-3 + x) * (3 + x)
(-3(3 + x) + x(3 + x)) + -8x = 0
((3 * -3 + x * -3) + x(3 + x)) + -8x = 0
((-9 + -3x) + x(3 + x)) + -8x = 0
(-9 + -3x + (3 * x + x * x)) + -8x = 0
(-9 + -3x + (3x + x2)) + -8x = 0

Combine like terms: -3x + 3x = 0
(-9 + 0 + x2) + -8x = 0
(-9 + x2) + -8x = 0

Reorder the terms:
-9 + -8x + x2 = 0

Solving
-9 + -8x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-1, 9}