2x(x+3)-7=5(5-x)+7(x+1)

Solution for 2x(x+3)-7=5(5-x)+7(x+1) equation:

Simplifying
2x(x + 3) + -7 = 5(5 + -1x) + 7(x + 1)

Reorder the terms:
2x(3 + x) + -7 = 5(5 + -1x) + 7(x + 1)
(3 * 2x + x * 2x) + -7 = 5(5 + -1x) + 7(x + 1)
(6x + 2x2) + -7 = 5(5 + -1x) + 7(x + 1)

Reorder the terms:
-7 + 6x + 2x2 = 5(5 + -1x) + 7(x + 1)
-7 + 6x + 2x2 = (5 * 5 + -1x * 5) + 7(x + 1)
-7 + 6x + 2x2 = (25 + -5x) + 7(x + 1)

Reorder the terms:
-7 + 6x + 2x2 = 25 + -5x + 7(1 + x)
-7 + 6x + 2x2 = 25 + -5x + (1 * 7 + x * 7)
-7 + 6x + 2x2 = 25 + -5x + (7 + 7x)

Reorder the terms:
-7 + 6x + 2x2 = 25 + 7 + -5x + 7x

Combine like terms: 25 + 7 = 32
-7 + 6x + 2x2 = 32 + -5x + 7x

Combine like terms: -5x + 7x = 2x
-7 + 6x + 2x2 = 32 + 2x

Solving
-7 + 6x + 2x2 = 32 + 2x

Solving for variable 'x'.

Reorder the terms:
-7 + -32 + 6x + -2x + 2x2 = 32 + 2x + -32 + -2x

Combine like terms: -7 + -32 = -39
-39 + 6x + -2x + 2x2 = 32 + 2x + -32 + -2x

Combine like terms: 6x + -2x = 4x
-39 + 4x + 2x2 = 32 + 2x + -32 + -2x

Reorder the terms:
-39 + 4x + 2x2 = 32 + -32 + 2x + -2x

Combine like terms: 32 + -32 = 0
-39 + 4x + 2x2 = 0 + 2x + -2x
-39 + 4x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-39 + 4x + 2x2 = 0

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

Divide each side by '2'.
-19.5 + 2x + x2 = 0

Move the constant term to the right:

Add '19.5' to each side of the equation.
-19.5 + 2x + 19.5 + x2 = 0 + 19.5

Reorder the terms:
-19.5 + 19.5 + 2x + x2 = 0 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + 2x + x2 = 0 + 19.5
2x + x2 = 0 + 19.5

Combine like terms: 0 + 19.5 = 19.5
2x + x2 = 19.5

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 = 19.5 + 1

Reorder the terms:
1 + 2x + x2 = 19.5 + 1

Combine like terms: 19.5 + 1 = 20.5
1 + 2x + x2 = 20.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 20.5

Calculate the square root of the right side: 4.527692569

Break this problem into two subproblems by setting 
(x + 1) equal to 4.527692569 and -4.527692569.

Subproblem 1
x + 1 = 4.527692569

Simplifying
x + 1 = 4.527692569

Reorder the terms:
1 + x = 4.527692569

Solving
1 + x = 4.527692569

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 = 4.527692569 + -1

Combine like terms: 1 + -1 = 0
0 + x = 4.527692569 + -1
x = 4.527692569 + -1

Combine like terms: 4.527692569 + -1 = 3.527692569
x = 3.527692569

Simplifying
x = 3.527692569

Subproblem 2
x + 1 = -4.527692569

Simplifying
x + 1 = -4.527692569

Reorder the terms:
1 + x = -4.527692569

Solving
1 + x = -4.527692569

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 = -4.527692569 + -1

Combine like terms: 1 + -1 = 0
0 + x = -4.527692569 + -1
x = -4.527692569 + -1

Combine like terms: -4.527692569 + -1 = -5.527692569
x = -5.527692569

Simplifying
x = -5.527692569

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.527692569, -5.527692569}