(10x+8)(x-1)=20

Solution for (10x+8)(x-1)=20 equation:

Simplifying
(10x + 8)(x + -1) = 20

Reorder the terms:
(8 + 10x)(x + -1) = 20

Reorder the terms:
(8 + 10x)(-1 + x) = 20

Multiply (8 + 10x) * (-1 + x)
(8(-1 + x) + 10x * (-1 + x)) = 20
((-1 * 8 + x * 8) + 10x * (-1 + x)) = 20
((-8 + 8x) + 10x * (-1 + x)) = 20
(-8 + 8x + (-1 * 10x + x * 10x)) = 20
(-8 + 8x + (-10x + 10x2)) = 20

Combine like terms: 8x + -10x = -2x
(-8 + -2x + 10x2) = 20

Solving
-8 + -2x + 10x2 = 20

Solving for variable 'x'.

Reorder the terms:
-8 + -20 + -2x + 10x2 = 20 + -20

Combine like terms: -8 + -20 = -28
-28 + -2x + 10x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-28 + -2x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + -1x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + -1x + 5x2)' equal to zero and attempt to solve:

Simplifying
-14 + -1x + 5x2 = 0

Solving
-14 + -1x + 5x2 = 0

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

Divide each side by '5'.
-2.8 + -0.2x + x2 = 0

Move the constant term to the right:

Add '2.8' to each side of the equation.
-2.8 + -0.2x + 2.8 + x2 = 0 + 2.8

Reorder the terms:
-2.8 + 2.8 + -0.2x + x2 = 0 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + -0.2x + x2 = 0 + 2.8
-0.2x + x2 = 0 + 2.8

Combine like terms: 0 + 2.8 = 2.8
-0.2x + x2 = 2.8

The x term is -0.2x.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2x + 0.01 + x2 = 2.8 + 0.01

Reorder the terms:
0.01 + -0.2x + x2 = 2.8 + 0.01

Combine like terms: 2.8 + 0.01 = 2.81
0.01 + -0.2x + x2 = 2.81

Factor a perfect square on the left side:
(x + -0.1)(x + -0.1) = 2.81

Calculate the square root of the right side: 1.676305461

Break this problem into two subproblems by setting 
(x + -0.1) equal to 1.676305461 and -1.676305461.

Subproblem 1
x + -0.1 = 1.676305461

Simplifying
x + -0.1 = 1.676305461

Reorder the terms:
-0.1 + x = 1.676305461

Solving
-0.1 + x = 1.676305461

Solving for variable 'x'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + x = 1.676305461 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + x = 1.676305461 + 0.1
x = 1.676305461 + 0.1

Combine like terms: 1.676305461 + 0.1 = 1.776305461
x = 1.776305461

Simplifying
x = 1.776305461

Subproblem 2
x + -0.1 = -1.676305461

Simplifying
x + -0.1 = -1.676305461

Reorder the terms:
-0.1 + x = -1.676305461

Solving
-0.1 + x = -1.676305461

Solving for variable 'x'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + x = -1.676305461 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + x = -1.676305461 + 0.1
x = -1.676305461 + 0.1

Combine like terms: -1.676305461 + 0.1 = -1.576305461
x = -1.576305461

Simplifying
x = -1.576305461

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.776305461, -1.576305461}
Solution
x = {1.776305461, -1.576305461}