(x-5)(x+5)=8x-41

Solution for (x-5)(x+5)=8x-41 equation:

Simplifying
(x + -5)(x + 5) = 8x + -41

Reorder the terms:
(-5 + x)(x + 5) = 8x + -41

Reorder the terms:
(-5 + x)(5 + x) = 8x + -41

Multiply (-5 + x) * (5 + x)
(-5(5 + x) + x(5 + x)) = 8x + -41
((5 * -5 + x * -5) + x(5 + x)) = 8x + -41
((-25 + -5x) + x(5 + x)) = 8x + -41
(-25 + -5x + (5 * x + x * x)) = 8x + -41
(-25 + -5x + (5x + x2)) = 8x + -41

Combine like terms: -5x + 5x = 0
(-25 + 0 + x2) = 8x + -41
(-25 + x2) = 8x + -41

Reorder the terms:
-25 + x2 = -41 + 8x

Solving
-25 + x2 = -41 + 8x

Solving for variable 'x'.

Reorder the terms:
-25 + 41 + -8x + x2 = -41 + 8x + 41 + -8x

Combine like terms: -25 + 41 = 16
16 + -8x + x2 = -41 + 8x + 41 + -8x

Reorder the terms:
16 + -8x + x2 = -41 + 41 + 8x + -8x

Combine like terms: -41 + 41 = 0
16 + -8x + x2 = 0 + 8x + -8x
16 + -8x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
16 + -8x + x2 = 0

Factor a trinomial.
(4 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {4, 4}