x(12-x)=27

Solution for x(12-x)=27 equation:

Simplifying
x(12 + -1x) = 27
(12 * x + -1x * x) = 27
(12x + -1x2) = 27

Solving
12x + -1x2 = 27

Solving for variable 'x'.

Reorder the terms:
-27 + 12x + -1x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 12x + -1x2 = 0

Factor a trinomial.
(-9 + x)(3 + -1x) = 0

Subproblem 1
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
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 = {9, 3}