x(27-x)=126

Solution for x(27-x)=126 equation:

Simplifying
x(27 + -1x) = 126
(27 * x + -1x * x) = 126
(27x + -1x2) = 126

Solving
27x + -1x2 = 126

Solving for variable 'x'.

Reorder the terms:
-126 + 27x + -1x2 = 126 + -126

Combine like terms: 126 + -126 = 0
-126 + 27x + -1x2 = 0

Factor a trinomial.
(-21 + x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-21 + x)' equal to zero and attempt to solve:

Simplifying
-21 + x = 0

Solving
-21 + x = 0

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

Add '21' to each side of the equation.
-21 + 21 + x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + x = 0 + 21
x = 0 + 21

Combine like terms: 0 + 21 = 21
x = 21

Simplifying
x = 21
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {21, 6}