3x(2x+7)-13=2x(7-x)

Solution for 3x(2x+7)-13=2x(7-x) equation:

Simplifying
3x(2x + 7) + -13 = 2x(7 + -1x)

Reorder the terms:
3x(7 + 2x) + -13 = 2x(7 + -1x)
(7 * 3x + 2x * 3x) + -13 = 2x(7 + -1x)
(21x + 6x2) + -13 = 2x(7 + -1x)

Reorder the terms:
-13 + 21x + 6x2 = 2x(7 + -1x)
-13 + 21x + 6x2 = (7 * 2x + -1x * 2x)
-13 + 21x + 6x2 = (14x + -2x2)

Solving
-13 + 21x + 6x2 = 14x + -2x2

Solving for variable 'x'.

Reorder the terms:
-13 + 21x + -14x + 6x2 + 2x2 = 14x + -2x2 + -14x + 2x2

Combine like terms: 21x + -14x = 7x
-13 + 7x + 6x2 + 2x2 = 14x + -2x2 + -14x + 2x2

Combine like terms: 6x2 + 2x2 = 8x2
-13 + 7x + 8x2 = 14x + -2x2 + -14x + 2x2

Reorder the terms:
-13 + 7x + 8x2 = 14x + -14x + -2x2 + 2x2

Combine like terms: 14x + -14x = 0
-13 + 7x + 8x2 = 0 + -2x2 + 2x2
-13 + 7x + 8x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-13 + 7x + 8x2 = 0

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

Divide each side by '8'.
-1.625 + 0.875x + x2 = 0

Move the constant term to the right:

Add '1.625' to each side of the equation.
-1.625 + 0.875x + 1.625 + x2 = 0 + 1.625

Reorder the terms:
-1.625 + 1.625 + 0.875x + x2 = 0 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + 0.875x + x2 = 0 + 1.625
0.875x + x2 = 0 + 1.625

Combine like terms: 0 + 1.625 = 1.625
0.875x + x2 = 1.625

The x term is 0.875x.  Take half its coefficient (0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
0.875x + 0.19140625 + x2 = 1.625 + 0.19140625

Reorder the terms:
0.19140625 + 0.875x + x2 = 1.625 + 0.19140625

Combine like terms: 1.625 + 0.19140625 = 1.81640625
0.19140625 + 0.875x + x2 = 1.81640625

Factor a perfect square on the left side:
(x + 0.4375)(x + 0.4375) = 1.81640625

Calculate the square root of the right side: 1.347741166

Break this problem into two subproblems by setting 
(x + 0.4375) equal to 1.347741166 and -1.347741166.

Subproblem 1
x + 0.4375 = 1.347741166

Simplifying
x + 0.4375 = 1.347741166

Reorder the terms:
0.4375 + x = 1.347741166

Solving
0.4375 + x = 1.347741166

Solving for variable 'x'.

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

Add '-0.4375' to each side of the equation.
0.4375 + -0.4375 + x = 1.347741166 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + x = 1.347741166 + -0.4375
x = 1.347741166 + -0.4375

Combine like terms: 1.347741166 + -0.4375 = 0.910241166
x = 0.910241166

Simplifying
x = 0.910241166

Subproblem 2
x + 0.4375 = -1.347741166

Simplifying
x + 0.4375 = -1.347741166

Reorder the terms:
0.4375 + x = -1.347741166

Solving
0.4375 + x = -1.347741166

Solving for variable 'x'.

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

Add '-0.4375' to each side of the equation.
0.4375 + -0.4375 + x = -1.347741166 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + x = -1.347741166 + -0.4375
x = -1.347741166 + -0.4375

Combine like terms: -1.347741166 + -0.4375 = -1.785241166
x = -1.785241166

Simplifying
x = -1.785241166

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.910241166, -1.785241166}