(5x)5(x-1)=10

Solution for (5x)5(x-1)=10 equation:

Simplifying
(5x) * 5(x + -1) = 10

Remove parenthesis around (5x)
5x * 5(x + -1) = 10

Reorder the terms:
5x * 5(-1 + x) = 10

Reorder the terms for easier multiplication:
5 * 5x(-1 + x) = 10

Multiply 5 * 5
25x(-1 + x) = 10
(-1 * 25x + x * 25x) = 10
(-25x + 25x2) = 10

Solving
-25x + 25x2 = 10

Solving for variable 'x'.

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

Combine like terms: 10 + -10 = 0
-10 + -25x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + -5x + 5x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-2 + -5x + 5x2)' equal to zero and attempt to solve:

Simplifying
-2 + -5x + 5x2 = 0

Solving
-2 + -5x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-0.4 + -1x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -1x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -1x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -1x + x2 = 0 + 0.4
-1x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-1x + x2 = 0.4

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 0.4 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.4 + 0.25

Combine like terms: 0.4 + 0.25 = 0.65
0.25 + -1x + x2 = 0.65

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.65

Calculate the square root of the right side: 0.806225775

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.806225775 and -0.806225775.

Subproblem 1
x + -0.5 = 0.806225775

Simplifying
x + -0.5 = 0.806225775

Reorder the terms:
-0.5 + x = 0.806225775

Solving
-0.5 + x = 0.806225775

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.806225775 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.806225775 + 0.5
x = 0.806225775 + 0.5

Combine like terms: 0.806225775 + 0.5 = 1.306225775
x = 1.306225775

Simplifying
x = 1.306225775

Subproblem 2
x + -0.5 = -0.806225775

Simplifying
x + -0.5 = -0.806225775

Reorder the terms:
-0.5 + x = -0.806225775

Solving
-0.5 + x = -0.806225775

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.806225775 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.806225775 + 0.5
x = -0.806225775 + 0.5

Combine like terms: -0.806225775 + 0.5 = -0.306225775
x = -0.306225775

Simplifying
x = -0.306225775

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.306225775, -0.306225775}
Solution
x = {1.306225775, -0.306225775}