40-4(x+3)=(5x)(x+1)

Solution for 40-4(x+3)=(5x)(x+1) equation:

Simplifying
40 + -4(x + 3) = (5x)(x + 1)

Reorder the terms:
40 + -4(3 + x) = (5x)(x + 1)
40 + (3 * -4 + x * -4) = (5x)(x + 1)
40 + (-12 + -4x) = (5x)(x + 1)

Combine like terms: 40 + -12 = 28
28 + -4x = (5x)(x + 1)

Remove parenthesis around (5x)
28 + -4x = 5x(x + 1)

Reorder the terms:
28 + -4x = 5x(1 + x)
28 + -4x = (1 * 5x + x * 5x)
28 + -4x = (5x + 5x2)

Solving
28 + -4x = 5x + 5x2

Solving for variable 'x'.

Combine like terms: -4x + -5x = -9x
28 + -9x + -5x2 = 5x + 5x2 + -5x + -5x2

Reorder the terms:
28 + -9x + -5x2 = 5x + -5x + 5x2 + -5x2

Combine like terms: 5x + -5x = 0
28 + -9x + -5x2 = 0 + 5x2 + -5x2
28 + -9x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
28 + -9x + -5x2 = 0

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

Divide each side by '-5'.
-5.6 + 1.8x + x2 = 0

Move the constant term to the right:

Add '5.6' to each side of the equation.
-5.6 + 1.8x + 5.6 + x2 = 0 + 5.6

Reorder the terms:
-5.6 + 5.6 + 1.8x + x2 = 0 + 5.6

Combine like terms: -5.6 + 5.6 = 0.0
0.0 + 1.8x + x2 = 0 + 5.6
1.8x + x2 = 0 + 5.6

Combine like terms: 0 + 5.6 = 5.6
1.8x + x2 = 5.6

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = 5.6 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = 5.6 + 0.81

Combine like terms: 5.6 + 0.81 = 6.41
0.81 + 1.8x + x2 = 6.41

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 6.41

Calculate the square root of the right side: 2.53179778

Break this problem into two subproblems by setting 
(x + 0.9) equal to 2.53179778 and -2.53179778.

Subproblem 1
x + 0.9 = 2.53179778

Simplifying
x + 0.9 = 2.53179778

Reorder the terms:
0.9 + x = 2.53179778

Solving
0.9 + x = 2.53179778

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = 2.53179778 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = 2.53179778 + -0.9
x = 2.53179778 + -0.9

Combine like terms: 2.53179778 + -0.9 = 1.63179778
x = 1.63179778

Simplifying
x = 1.63179778

Subproblem 2
x + 0.9 = -2.53179778

Simplifying
x + 0.9 = -2.53179778

Reorder the terms:
0.9 + x = -2.53179778

Solving
0.9 + x = -2.53179778

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = -2.53179778 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = -2.53179778 + -0.9
x = -2.53179778 + -0.9

Combine like terms: -2.53179778 + -0.9 = -3.43179778
x = -3.43179778

Simplifying
x = -3.43179778

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.63179778, -3.43179778}