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

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

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

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

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

Multiply (3 + u) * (-3 + u)
(3(-3 + u) + u(-3 + u)) + -8u = 0
((-3 * 3 + u * 3) + u(-3 + u)) + -8u = 0
((-9 + 3u) + u(-3 + u)) + -8u = 0
(-9 + 3u + (-3 * u + u * u)) + -8u = 0
(-9 + 3u + (-3u + u2)) + -8u = 0

Combine like terms: 3u + -3u = 0
(-9 + 0 + u2) + -8u = 0
(-9 + u2) + -8u = 0

Reorder the terms:
-9 + -8u + u2 = 0

Solving
-9 + -8u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-1 + -1u)(9 + -1u) = 0

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

Simplifying
-1 + -1u = 0

Solving
-1 + -1u = 0

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

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

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

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

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

Simplifying
u = -1
Subproblem 2
Set the factor '(9 + -1u)' equal to zero and attempt to solve:

Simplifying
9 + -1u = 0

Solving
9 + -1u = 0

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

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

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

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

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

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