(x-5)*(x-5)=x-3

Solution for (x-5)*(x-5)=x-3 equation:

Simplifying
(x + -5)(x + -5) = x + -3

Reorder the terms:
(-5 + x)(x + -5) = x + -3

Reorder the terms:
(-5 + x)(-5 + x) = x + -3

Multiply (-5 + x) * (-5 + x)
(-5(-5 + x) + x(-5 + x)) = x + -3
((-5 * -5 + x * -5) + x(-5 + x)) = x + -3
((25 + -5x) + x(-5 + x)) = x + -3
(25 + -5x + (-5 * x + x * x)) = x + -3
(25 + -5x + (-5x + x2)) = x + -3

Combine like terms: -5x + -5x = -10x
(25 + -10x + x2) = x + -3

Reorder the terms:
25 + -10x + x2 = -3 + x

Solving
25 + -10x + x2 = -3 + x

Solving for variable 'x'.

Reorder the terms:
25 + 3 + -10x + -1x + x2 = -3 + x + 3 + -1x

Combine like terms: 25 + 3 = 28
28 + -10x + -1x + x2 = -3 + x + 3 + -1x

Combine like terms: -10x + -1x = -11x
28 + -11x + x2 = -3 + x + 3 + -1x

Reorder the terms:
28 + -11x + x2 = -3 + 3 + x + -1x

Combine like terms: -3 + 3 = 0
28 + -11x + x2 = 0 + x + -1x
28 + -11x + x2 = x + -1x

Combine like terms: x + -1x = 0
28 + -11x + x2 = 0

Factor a trinomial.
(4 + -1x)(7 + -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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {4, 7}