5x(x-1)=x+3

Solution for 5x(x-1)=x+3 equation:

Simplifying
5x(x + -1) = x + 3

Reorder the terms:
5x(-1 + x) = x + 3
(-1 * 5x + x * 5x) = x + 3
(-5x + 5x2) = x + 3

Reorder the terms:
-5x + 5x2 = 3 + x

Solving
-5x + 5x2 = 3 + x

Solving for variable 'x'.

Reorder the terms:
-3 + -5x + -1x + 5x2 = 3 + x + -3 + -1x

Combine like terms: -5x + -1x = -6x
-3 + -6x + 5x2 = 3 + x + -3 + -1x

Reorder the terms:
-3 + -6x + 5x2 = 3 + -3 + x + -1x

Combine like terms: 3 + -3 = 0
-3 + -6x + 5x2 = 0 + x + -1x
-3 + -6x + 5x2 = x + -1x

Combine like terms: x + -1x = 0
-3 + -6x + 5x2 = 0

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

Divide each side by '5'.
-0.6 + -1.2x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -1.2x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -1.2x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -1.2x + x2 = 0 + 0.6
-1.2x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-1.2x + x2 = 0.6

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = 0.6 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = 0.6 + 0.36

Combine like terms: 0.6 + 0.36 = 0.96
0.36 + -1.2x + x2 = 0.96

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 0.96

Calculate the square root of the right side: 0.979795897

Break this problem into two subproblems by setting 
(x + -0.6) equal to 0.979795897 and -0.979795897.

Subproblem 1
x + -0.6 = 0.979795897

Simplifying
x + -0.6 = 0.979795897

Reorder the terms:
-0.6 + x = 0.979795897

Solving
-0.6 + x = 0.979795897

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x = 0.979795897 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x = 0.979795897 + 0.6
x = 0.979795897 + 0.6

Combine like terms: 0.979795897 + 0.6 = 1.579795897
x = 1.579795897

Simplifying
x = 1.579795897

Subproblem 2
x + -0.6 = -0.979795897

Simplifying
x + -0.6 = -0.979795897

Reorder the terms:
-0.6 + x = -0.979795897

Solving
-0.6 + x = -0.979795897

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x = -0.979795897 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x = -0.979795897 + 0.6
x = -0.979795897 + 0.6

Combine like terms: -0.979795897 + 0.6 = -0.379795897
x = -0.379795897

Simplifying
x = -0.379795897

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.579795897, -0.379795897}