x(6-x)+1=-26

Solution for x(6-x)+1=-26 equation:

Simplifying
x(6 + -1x) + 1 = -26
(6 * x + -1x * x) + 1 = -26
(6x + -1x2) + 1 = -26

Reorder the terms:
1 + 6x + -1x2 = -26

Solving
1 + 6x + -1x2 = -26

Solving for variable 'x'.

Reorder the terms:
1 + 26 + 6x + -1x2 = -26 + 26

Combine like terms: 1 + 26 = 27
27 + 6x + -1x2 = -26 + 26

Combine like terms: -26 + 26 = 0
27 + 6x + -1x2 = 0

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

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

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

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

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

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {9, -3}