(x+5)(x-5)=11x+1

Solution for (x+5)(x-5)=11x+1 equation:

Simplifying
(x + 5)(x + -5) = 11x + 1

Reorder the terms:
(5 + x)(x + -5) = 11x + 1

Reorder the terms:
(5 + x)(-5 + x) = 11x + 1

Multiply (5 + x) * (-5 + x)
(5(-5 + x) + x(-5 + x)) = 11x + 1
((-5 * 5 + x * 5) + x(-5 + x)) = 11x + 1
((-25 + 5x) + x(-5 + x)) = 11x + 1
(-25 + 5x + (-5 * x + x * x)) = 11x + 1
(-25 + 5x + (-5x + x2)) = 11x + 1

Combine like terms: 5x + -5x = 0
(-25 + 0 + x2) = 11x + 1
(-25 + x2) = 11x + 1

Reorder the terms:
-25 + x2 = 1 + 11x

Solving
-25 + x2 = 1 + 11x

Solving for variable 'x'.

Reorder the terms:
-25 + -1 + -11x + x2 = 1 + 11x + -1 + -11x

Combine like terms: -25 + -1 = -26
-26 + -11x + x2 = 1 + 11x + -1 + -11x

Reorder the terms:
-26 + -11x + x2 = 1 + -1 + 11x + -11x

Combine like terms: 1 + -1 = 0
-26 + -11x + x2 = 0 + 11x + -11x
-26 + -11x + x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
-26 + -11x + x2 = 0

Factor a trinomial.
(-2 + -1x)(13 + -1x) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-2, 13}