(2x+3)(x-2)+(8x-1)(x+1)=0

Solution for (2x+3)(x-2)+(8x-1)(x+1)=0 equation:

Simplifying
(2x + 3)(x + -2) + (8x + -1)(x + 1) = 0

Reorder the terms:
(3 + 2x)(x + -2) + (8x + -1)(x + 1) = 0

Reorder the terms:
(3 + 2x)(-2 + x) + (8x + -1)(x + 1) = 0

Multiply (3 + 2x) * (-2 + x)
(3(-2 + x) + 2x * (-2 + x)) + (8x + -1)(x + 1) = 0
((-2 * 3 + x * 3) + 2x * (-2 + x)) + (8x + -1)(x + 1) = 0
((-6 + 3x) + 2x * (-2 + x)) + (8x + -1)(x + 1) = 0
(-6 + 3x + (-2 * 2x + x * 2x)) + (8x + -1)(x + 1) = 0
(-6 + 3x + (-4x + 2x2)) + (8x + -1)(x + 1) = 0

Combine like terms: 3x + -4x = -1x
(-6 + -1x + 2x2) + (8x + -1)(x + 1) = 0

Reorder the terms:
-6 + -1x + 2x2 + (-1 + 8x)(x + 1) = 0

Reorder the terms:
-6 + -1x + 2x2 + (-1 + 8x)(1 + x) = 0

Multiply (-1 + 8x) * (1 + x)
-6 + -1x + 2x2 + (-1(1 + x) + 8x * (1 + x)) = 0
-6 + -1x + 2x2 + ((1 * -1 + x * -1) + 8x * (1 + x)) = 0
-6 + -1x + 2x2 + ((-1 + -1x) + 8x * (1 + x)) = 0
-6 + -1x + 2x2 + (-1 + -1x + (1 * 8x + x * 8x)) = 0
-6 + -1x + 2x2 + (-1 + -1x + (8x + 8x2)) = 0

Combine like terms: -1x + 8x = 7x
-6 + -1x + 2x2 + (-1 + 7x + 8x2) = 0

Reorder the terms:
-6 + -1 + -1x + 7x + 2x2 + 8x2 = 0

Combine like terms: -6 + -1 = -7
-7 + -1x + 7x + 2x2 + 8x2 = 0

Combine like terms: -1x + 7x = 6x
-7 + 6x + 2x2 + 8x2 = 0

Combine like terms: 2x2 + 8x2 = 10x2
-7 + 6x + 10x2 = 0

Solving
-7 + 6x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
-0.7 + 0.6x + x2 = 0.0

Move the constant term to the right:

Add '0.7' to each side of the equation.
-0.7 + 0.6x + 0.7 + x2 = 0.0 + 0.7

Reorder the terms:
-0.7 + 0.7 + 0.6x + x2 = 0.0 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + 0.6x + x2 = 0.0 + 0.7
0.6x + x2 = 0.0 + 0.7

Combine like terms: 0.0 + 0.7 = 0.7
0.6x + x2 = 0.7

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = 0.7 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 0.7 + 0.09

Combine like terms: 0.7 + 0.09 = 0.79
0.09 + 0.6x + x2 = 0.79

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 0.79

Calculate the square root of the right side: 0.888819442

Break this problem into two subproblems by setting 
(x + 0.3) equal to 0.888819442 and -0.888819442.

Subproblem 1
x + 0.3 = 0.888819442

Simplifying
x + 0.3 = 0.888819442

Reorder the terms:
0.3 + x = 0.888819442

Solving
0.3 + x = 0.888819442

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = 0.888819442 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = 0.888819442 + -0.3
x = 0.888819442 + -0.3

Combine like terms: 0.888819442 + -0.3 = 0.588819442
x = 0.588819442

Simplifying
x = 0.588819442

Subproblem 2
x + 0.3 = -0.888819442

Simplifying
x + 0.3 = -0.888819442

Reorder the terms:
0.3 + x = -0.888819442

Solving
0.3 + x = -0.888819442

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = -0.888819442 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = -0.888819442 + -0.3
x = -0.888819442 + -0.3

Combine like terms: -0.888819442 + -0.3 = -1.188819442
x = -1.188819442

Simplifying
x = -1.188819442

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.588819442, -1.188819442}