x(2x+7)-5=(x+4)(5-x)

Solution for x(2x+7)-5=(x+4)(5-x) equation:

Simplifying
x(2x + 7) + -5 = (x + 4)(5 + -1x)

Reorder the terms:
x(7 + 2x) + -5 = (x + 4)(5 + -1x)
(7 * x + 2x * x) + -5 = (x + 4)(5 + -1x)
(7x + 2x2) + -5 = (x + 4)(5 + -1x)

Reorder the terms:
-5 + 7x + 2x2 = (x + 4)(5 + -1x)

Reorder the terms:
-5 + 7x + 2x2 = (4 + x)(5 + -1x)

Multiply (4 + x) * (5 + -1x)
-5 + 7x + 2x2 = (4(5 + -1x) + x(5 + -1x))
-5 + 7x + 2x2 = ((5 * 4 + -1x * 4) + x(5 + -1x))
-5 + 7x + 2x2 = ((20 + -4x) + x(5 + -1x))
-5 + 7x + 2x2 = (20 + -4x + (5 * x + -1x * x))
-5 + 7x + 2x2 = (20 + -4x + (5x + -1x2))

Combine like terms: -4x + 5x = 1x
-5 + 7x + 2x2 = (20 + 1x + -1x2)

Solving
-5 + 7x + 2x2 = 20 + 1x + -1x2

Solving for variable 'x'.

Reorder the terms:
-5 + -20 + 7x + -1x + 2x2 + x2 = 20 + 1x + -1x2 + -20 + -1x + x2

Combine like terms: -5 + -20 = -25
-25 + 7x + -1x + 2x2 + x2 = 20 + 1x + -1x2 + -20 + -1x + x2

Combine like terms: 7x + -1x = 6x
-25 + 6x + 2x2 + x2 = 20 + 1x + -1x2 + -20 + -1x + x2

Combine like terms: 2x2 + x2 = 3x2
-25 + 6x + 3x2 = 20 + 1x + -1x2 + -20 + -1x + x2

Reorder the terms:
-25 + 6x + 3x2 = 20 + -20 + 1x + -1x + -1x2 + x2

Combine like terms: 20 + -20 = 0
-25 + 6x + 3x2 = 0 + 1x + -1x + -1x2 + x2
-25 + 6x + 3x2 = 1x + -1x + -1x2 + x2

Combine like terms: 1x + -1x = 0
-25 + 6x + 3x2 = 0 + -1x2 + x2
-25 + 6x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-25 + 6x + 3x2 = 0

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

Divide each side by '3'.
-8.333333333 + 2x + x2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + 2x + 8.333333333 + x2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + 2x + x2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + 2x + x2 = 0 + 8.333333333
2x + x2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
2x + x2 = 8.333333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 8.333333333 + 1

Reorder the terms:
1 + 2x + x2 = 8.333333333 + 1

Combine like terms: 8.333333333 + 1 = 9.333333333
1 + 2x + x2 = 9.333333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 9.333333333

Calculate the square root of the right side: 3.055050463

Break this problem into two subproblems by setting 
(x + 1) equal to 3.055050463 and -3.055050463.

Subproblem 1
x + 1 = 3.055050463

Simplifying
x + 1 = 3.055050463

Reorder the terms:
1 + x = 3.055050463

Solving
1 + x = 3.055050463

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 3.055050463 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.055050463 + -1
x = 3.055050463 + -1

Combine like terms: 3.055050463 + -1 = 2.055050463
x = 2.055050463

Simplifying
x = 2.055050463

Subproblem 2
x + 1 = -3.055050463

Simplifying
x + 1 = -3.055050463

Reorder the terms:
1 + x = -3.055050463

Solving
1 + x = -3.055050463

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -3.055050463 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.055050463 + -1
x = -3.055050463 + -1

Combine like terms: -3.055050463 + -1 = -4.055050463
x = -4.055050463

Simplifying
x = -4.055050463

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.055050463, -4.055050463}