x+9=(x-9)(x+9)

Solution for x+9=(x-9)(x+9) equation:

Simplifying
x + 9 = (x + -9)(x + 9)

Reorder the terms:
9 + x = (x + -9)(x + 9)

Reorder the terms:
9 + x = (-9 + x)(x + 9)

Reorder the terms:
9 + x = (-9 + x)(9 + x)

Multiply (-9 + x) * (9 + x)
9 + x = (-9(9 + x) + x(9 + x))
9 + x = ((9 * -9 + x * -9) + x(9 + x))
9 + x = ((-81 + -9x) + x(9 + x))
9 + x = (-81 + -9x + (9 * x + x * x))
9 + x = (-81 + -9x + (9x + x2))

Combine like terms: -9x + 9x = 0
9 + x = (-81 + 0 + x2)
9 + x = (-81 + x2)

Solving
9 + x = -81 + x2

Solving for variable 'x'.

Reorder the terms:
9 + 81 + x + -1x2 = -81 + x2 + 81 + -1x2

Combine like terms: 9 + 81 = 90
90 + x + -1x2 = -81 + x2 + 81 + -1x2

Reorder the terms:
90 + x + -1x2 = -81 + 81 + x2 + -1x2

Combine like terms: -81 + 81 = 0
90 + x + -1x2 = 0 + x2 + -1x2
90 + x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
90 + x + -1x2 = 0

Factor a trinomial.
(10 + -1x)(9 + x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 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 + x = 0 + -9

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

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

Simplifying
x = -9
Solution
x = {10, -9}