(x-5)(2-3x)=x(4x+7)-(2x+6)

Solution for (x-5)(2-3x)=x(4x+7)-(2x+6) equation:

Simplifying
(x + -5)(2 + -3x) = x(4x + 7) + -1(2x + 6)

Reorder the terms:
(-5 + x)(2 + -3x) = x(4x + 7) + -1(2x + 6)

Multiply (-5 + x) * (2 + -3x)
(-5(2 + -3x) + x(2 + -3x)) = x(4x + 7) + -1(2x + 6)
((2 * -5 + -3x * -5) + x(2 + -3x)) = x(4x + 7) + -1(2x + 6)
((-10 + 15x) + x(2 + -3x)) = x(4x + 7) + -1(2x + 6)
(-10 + 15x + (2 * x + -3x * x)) = x(4x + 7) + -1(2x + 6)
(-10 + 15x + (2x + -3x2)) = x(4x + 7) + -1(2x + 6)

Combine like terms: 15x + 2x = 17x
(-10 + 17x + -3x2) = x(4x + 7) + -1(2x + 6)

Reorder the terms:
-10 + 17x + -3x2 = x(7 + 4x) + -1(2x + 6)
-10 + 17x + -3x2 = (7 * x + 4x * x) + -1(2x + 6)
-10 + 17x + -3x2 = (7x + 4x2) + -1(2x + 6)

Reorder the terms:
-10 + 17x + -3x2 = 7x + 4x2 + -1(6 + 2x)
-10 + 17x + -3x2 = 7x + 4x2 + (6 * -1 + 2x * -1)
-10 + 17x + -3x2 = 7x + 4x2 + (-6 + -2x)

Reorder the terms:
-10 + 17x + -3x2 = -6 + 7x + -2x + 4x2

Combine like terms: 7x + -2x = 5x
-10 + 17x + -3x2 = -6 + 5x + 4x2

Solving
-10 + 17x + -3x2 = -6 + 5x + 4x2

Solving for variable 'x'.

Reorder the terms:
-10 + 6 + 17x + -5x + -3x2 + -4x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2

Combine like terms: -10 + 6 = -4
-4 + 17x + -5x + -3x2 + -4x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2

Combine like terms: 17x + -5x = 12x
-4 + 12x + -3x2 + -4x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2

Combine like terms: -3x2 + -4x2 = -7x2
-4 + 12x + -7x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2

Reorder the terms:
-4 + 12x + -7x2 = -6 + 6 + 5x + -5x + 4x2 + -4x2

Combine like terms: -6 + 6 = 0
-4 + 12x + -7x2 = 0 + 5x + -5x + 4x2 + -4x2
-4 + 12x + -7x2 = 5x + -5x + 4x2 + -4x2

Combine like terms: 5x + -5x = 0
-4 + 12x + -7x2 = 0 + 4x2 + -4x2
-4 + 12x + -7x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-4 + 12x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
0.5714285714 + -1.714285714x + x2 = 0

Move the constant term to the right:

Add '-0.5714285714' to each side of the equation.
0.5714285714 + -1.714285714x + -0.5714285714 + x2 = 0 + -0.5714285714

Reorder the terms:
0.5714285714 + -0.5714285714 + -1.714285714x + x2 = 0 + -0.5714285714

Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000
0.0000000000 + -1.714285714x + x2 = 0 + -0.5714285714
-1.714285714x + x2 = 0 + -0.5714285714

Combine like terms: 0 + -0.5714285714 = -0.5714285714
-1.714285714x + x2 = -0.5714285714

The x term is -1.714285714x.  Take half its coefficient (-0.857142857).
Square it (0.7346938773) and add it to both sides.

Add '0.7346938773' to each side of the equation.
-1.714285714x + 0.7346938773 + x2 = -0.5714285714 + 0.7346938773

Reorder the terms:
0.7346938773 + -1.714285714x + x2 = -0.5714285714 + 0.7346938773

Combine like terms: -0.5714285714 + 0.7346938773 = 0.1632653059
0.7346938773 + -1.714285714x + x2 = 0.1632653059

Factor a perfect square on the left side:
(x + -0.857142857)(x + -0.857142857) = 0.1632653059

Calculate the square root of the right side: 0.404061018

Break this problem into two subproblems by setting 
(x + -0.857142857) equal to 0.404061018 and -0.404061018.

Subproblem 1
x + -0.857142857 = 0.404061018

Simplifying
x + -0.857142857 = 0.404061018

Reorder the terms:
-0.857142857 + x = 0.404061018

Solving
-0.857142857 + x = 0.404061018

Solving for variable 'x'.

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

Add '0.857142857' to each side of the equation.
-0.857142857 + 0.857142857 + x = 0.404061018 + 0.857142857

Combine like terms: -0.857142857 + 0.857142857 = 0.000000000
0.000000000 + x = 0.404061018 + 0.857142857
x = 0.404061018 + 0.857142857

Combine like terms: 0.404061018 + 0.857142857 = 1.261203875
x = 1.261203875

Simplifying
x = 1.261203875

Subproblem 2
x + -0.857142857 = -0.404061018

Simplifying
x + -0.857142857 = -0.404061018

Reorder the terms:
-0.857142857 + x = -0.404061018

Solving
-0.857142857 + x = -0.404061018

Solving for variable 'x'.

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

Add '0.857142857' to each side of the equation.
-0.857142857 + 0.857142857 + x = -0.404061018 + 0.857142857

Combine like terms: -0.857142857 + 0.857142857 = 0.000000000
0.000000000 + x = -0.404061018 + 0.857142857
x = -0.404061018 + 0.857142857

Combine like terms: -0.404061018 + 0.857142857 = 0.453081839
x = 0.453081839

Simplifying
x = 0.453081839

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.261203875, 0.453081839}