9=x(6-x)

Solution for 9=x(6-x) equation:

Simplifying
9 = x(6 + -1x)
9 = (6 * x + -1x * x)
9 = (6x + -1x2)

Solving
9 = 6x + -1x2

Solving for variable 'x'.

Reorder the terms:
9 + -6x + x2 = 6x + -6x + -1x2 + x2

Combine like terms: 6x + -6x = 0
9 + -6x + x2 = 0 + -1x2 + x2
9 + -6x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
9 + -6x + x2 = 0

Factor a trinomial.
(3 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {3, 3}