(8x+10)(10x+9)=32

Solution for (8x+10)(10x+9)=32 equation:

Simplifying
(8x + 10)(10x + 9) = 32

Reorder the terms:
(10 + 8x)(10x + 9) = 32

Reorder the terms:
(10 + 8x)(9 + 10x) = 32

Multiply (10 + 8x) * (9 + 10x)
(10(9 + 10x) + 8x * (9 + 10x)) = 32
((9 * 10 + 10x * 10) + 8x * (9 + 10x)) = 32
((90 + 100x) + 8x * (9 + 10x)) = 32
(90 + 100x + (9 * 8x + 10x * 8x)) = 32
(90 + 100x + (72x + 80x2)) = 32

Combine like terms: 100x + 72x = 172x
(90 + 172x + 80x2) = 32

Solving
90 + 172x + 80x2 = 32

Solving for variable 'x'.

Reorder the terms:
90 + -32 + 172x + 80x2 = 32 + -32

Combine like terms: 90 + -32 = 58
58 + 172x + 80x2 = 32 + -32

Combine like terms: 32 + -32 = 0
58 + 172x + 80x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(29 + 86x + 40x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(29 + 86x + 40x2)' equal to zero and attempt to solve:

Simplifying
29 + 86x + 40x2 = 0

Solving
29 + 86x + 40x2 = 0

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

Divide each side by '40'.
0.725 + 2.15x + x2 = 0.0

Move the constant term to the right:

Add '-0.725' to each side of the equation.
0.725 + 2.15x + -0.725 + x2 = 0.0 + -0.725

Reorder the terms:
0.725 + -0.725 + 2.15x + x2 = 0.0 + -0.725

Combine like terms: 0.725 + -0.725 = 0.000
0.000 + 2.15x + x2 = 0.0 + -0.725
2.15x + x2 = 0.0 + -0.725

Combine like terms: 0.0 + -0.725 = -0.725
2.15x + x2 = -0.725

The x term is 2.15x.  Take half its coefficient (1.075).
Square it (1.155625) and add it to both sides.

Add '1.155625' to each side of the equation.
2.15x + 1.155625 + x2 = -0.725 + 1.155625

Reorder the terms:
1.155625 + 2.15x + x2 = -0.725 + 1.155625

Combine like terms: -0.725 + 1.155625 = 0.430625
1.155625 + 2.15x + x2 = 0.430625

Factor a perfect square on the left side:
(x + 1.075)(x + 1.075) = 0.430625

Calculate the square root of the right side: 0.656220237

Break this problem into two subproblems by setting 
(x + 1.075) equal to 0.656220237 and -0.656220237.

Subproblem 1
x + 1.075 = 0.656220237

Simplifying
x + 1.075 = 0.656220237

Reorder the terms:
1.075 + x = 0.656220237

Solving
1.075 + x = 0.656220237

Solving for variable 'x'.

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

Add '-1.075' to each side of the equation.
1.075 + -1.075 + x = 0.656220237 + -1.075

Combine like terms: 1.075 + -1.075 = 0.000
0.000 + x = 0.656220237 + -1.075
x = 0.656220237 + -1.075

Combine like terms: 0.656220237 + -1.075 = -0.418779763
x = -0.418779763

Simplifying
x = -0.418779763

Subproblem 2
x + 1.075 = -0.656220237

Simplifying
x + 1.075 = -0.656220237

Reorder the terms:
1.075 + x = -0.656220237

Solving
1.075 + x = -0.656220237

Solving for variable 'x'.

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

Add '-1.075' to each side of the equation.
1.075 + -1.075 + x = -0.656220237 + -1.075

Combine like terms: 1.075 + -1.075 = 0.000
0.000 + x = -0.656220237 + -1.075
x = -0.656220237 + -1.075

Combine like terms: -0.656220237 + -1.075 = -1.731220237
x = -1.731220237

Simplifying
x = -1.731220237

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.418779763, -1.731220237}
Solution
x = {-0.418779763, -1.731220237}