x-(4x-7)=5x-x(x+21)

Solution for x-(4x-7)=5x-x(x+21) equation:

Simplifying
x + -1(4x + -7) = 5x + -1x(x + 21)

Reorder the terms:
x + -1(-7 + 4x) = 5x + -1x(x + 21)
x + (-7 * -1 + 4x * -1) = 5x + -1x(x + 21)
x + (7 + -4x) = 5x + -1x(x + 21)

Reorder the terms:
7 + x + -4x = 5x + -1x(x + 21)

Combine like terms: x + -4x = -3x
7 + -3x = 5x + -1x(x + 21)

Reorder the terms:
7 + -3x = 5x + -1x(21 + x)
7 + -3x = 5x + (21 * -1x + x * -1x)
7 + -3x = 5x + (-21x + -1x2)

Combine like terms: 5x + -21x = -16x
7 + -3x = -16x + -1x2

Solving
7 + -3x = -16x + -1x2

Solving for variable 'x'.

Combine like terms: -3x + 16x = 13x
7 + 13x + x2 = -16x + -1x2 + 16x + x2

Reorder the terms:
7 + 13x + x2 = -16x + 16x + -1x2 + x2

Combine like terms: -16x + 16x = 0
7 + 13x + x2 = 0 + -1x2 + x2
7 + 13x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
7 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 13x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 13x + x2 = 0 + -7

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

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

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = -7 + 42.25

Reorder the terms:
42.25 + 13x + x2 = -7 + 42.25

Combine like terms: -7 + 42.25 = 35.25
42.25 + 13x + x2 = 35.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 35.25

Calculate the square root of the right side: 5.937171044

Break this problem into two subproblems by setting 
(x + 6.5) equal to 5.937171044 and -5.937171044.

Subproblem 1
x + 6.5 = 5.937171044

Simplifying
x + 6.5 = 5.937171044

Reorder the terms:
6.5 + x = 5.937171044

Solving
6.5 + x = 5.937171044

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 5.937171044 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 5.937171044 + -6.5
x = 5.937171044 + -6.5

Combine like terms: 5.937171044 + -6.5 = -0.562828956
x = -0.562828956

Simplifying
x = -0.562828956

Subproblem 2
x + 6.5 = -5.937171044

Simplifying
x + 6.5 = -5.937171044

Reorder the terms:
6.5 + x = -5.937171044

Solving
6.5 + x = -5.937171044

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -5.937171044 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -5.937171044 + -6.5
x = -5.937171044 + -6.5

Combine like terms: -5.937171044 + -6.5 = -12.437171044
x = -12.437171044

Simplifying
x = -12.437171044

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.562828956, -12.437171044}