9(x-1)-8x(1-x)-7x=20

Solution for 9(x-1)-8x(1-x)-7x=20 equation:

Simplifying
9(x + -1) + -8x(1 + -1x) + -7x = 20

Reorder the terms:
9(-1 + x) + -8x(1 + -1x) + -7x = 20
(-1 * 9 + x * 9) + -8x(1 + -1x) + -7x = 20
(-9 + 9x) + -8x(1 + -1x) + -7x = 20
-9 + 9x + (1 * -8x + -1x * -8x) + -7x = 20
-9 + 9x + (-8x + 8x2) + -7x = 20

Reorder the terms:
-9 + 9x + -8x + -7x + 8x2 = 20

Combine like terms: 9x + -8x = 1x
-9 + 1x + -7x + 8x2 = 20

Combine like terms: 1x + -7x = -6x
-9 + -6x + 8x2 = 20

Solving
-9 + -6x + 8x2 = 20

Solving for variable 'x'.

Reorder the terms:
-9 + -20 + -6x + 8x2 = 20 + -20

Combine like terms: -9 + -20 = -29
-29 + -6x + 8x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-29 + -6x + 8x2 = 0

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

Divide each side by '8'.
-3.625 + -0.75x + x2 = 0

Move the constant term to the right:

Add '3.625' to each side of the equation.
-3.625 + -0.75x + 3.625 + x2 = 0 + 3.625

Reorder the terms:
-3.625 + 3.625 + -0.75x + x2 = 0 + 3.625

Combine like terms: -3.625 + 3.625 = 0.000
0.000 + -0.75x + x2 = 0 + 3.625
-0.75x + x2 = 0 + 3.625

Combine like terms: 0 + 3.625 = 3.625
-0.75x + x2 = 3.625

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 3.625 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 3.625 + 0.140625

Combine like terms: 3.625 + 0.140625 = 3.765625
0.140625 + -0.75x + x2 = 3.765625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 3.765625

Calculate the square root of the right side: 1.940521837

Break this problem into two subproblems by setting 
(x + -0.375) equal to 1.940521837 and -1.940521837.

Subproblem 1
x + -0.375 = 1.940521837

Simplifying
x + -0.375 = 1.940521837

Reorder the terms:
-0.375 + x = 1.940521837

Solving
-0.375 + x = 1.940521837

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 1.940521837 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 1.940521837 + 0.375
x = 1.940521837 + 0.375

Combine like terms: 1.940521837 + 0.375 = 2.315521837
x = 2.315521837

Simplifying
x = 2.315521837

Subproblem 2
x + -0.375 = -1.940521837

Simplifying
x + -0.375 = -1.940521837

Reorder the terms:
-0.375 + x = -1.940521837

Solving
-0.375 + x = -1.940521837

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -1.940521837 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -1.940521837 + 0.375
x = -1.940521837 + 0.375

Combine like terms: -1.940521837 + 0.375 = -1.565521837
x = -1.565521837

Simplifying
x = -1.565521837

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.315521837, -1.565521837}