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

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

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

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

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

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

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

Solving
-5 + 5x2 = x

Solving for variable 'x'.

Reorder the terms:
-5 + -1x + 5x2 = x + -1x

Combine like terms: x + -1x = 0
-5 + -1x + 5x2 = 0

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

Divide each side by '5'.
-1 + -0.2x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.2x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.2x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.2x + x2 = 0 + 1
-0.2x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.2x + x2 = 1

The x term is -0.2x.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2x + 0.01 + x2 = 1 + 0.01

Reorder the terms:
0.01 + -0.2x + x2 = 1 + 0.01

Combine like terms: 1 + 0.01 = 1.01
0.01 + -0.2x + x2 = 1.01

Factor a perfect square on the left side:
(x + -0.1)(x + -0.1) = 1.01

Calculate the square root of the right side: 1.004987562

Break this problem into two subproblems by setting 
(x + -0.1) equal to 1.004987562 and -1.004987562.

Subproblem 1
x + -0.1 = 1.004987562

Simplifying
x + -0.1 = 1.004987562

Reorder the terms:
-0.1 + x = 1.004987562

Solving
-0.1 + x = 1.004987562

Solving for variable 'x'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + x = 1.004987562 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + x = 1.004987562 + 0.1
x = 1.004987562 + 0.1

Combine like terms: 1.004987562 + 0.1 = 1.104987562
x = 1.104987562

Simplifying
x = 1.104987562

Subproblem 2
x + -0.1 = -1.004987562

Simplifying
x + -0.1 = -1.004987562

Reorder the terms:
-0.1 + x = -1.004987562

Solving
-0.1 + x = -1.004987562

Solving for variable 'x'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + x = -1.004987562 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + x = -1.004987562 + 0.1
x = -1.004987562 + 0.1

Combine like terms: -1.004987562 + 0.1 = -0.904987562
x = -0.904987562

Simplifying
x = -0.904987562

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.104987562, -0.904987562}