x(26-x)=69

Solution for x(26-x)=69 equation:

Simplifying
x(26 + -1x) = 69
(26 * x + -1x * x) = 69
(26x + -1x2) = 69

Solving
26x + -1x2 = 69

Solving for variable 'x'.

Reorder the terms:
-69 + 26x + -1x2 = 69 + -69

Combine like terms: 69 + -69 = 0
-69 + 26x + -1x2 = 0

Factor a trinomial.
(-23 + x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-23 + x)' equal to zero and attempt to solve:

Simplifying
-23 + x = 0

Solving
-23 + x = 0

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

Add '23' to each side of the equation.
-23 + 23 + x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + x = 0 + 23
x = 0 + 23

Combine like terms: 0 + 23 = 23
x = 23

Simplifying
x = 23
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 = {23, 3}