(2x+3)(x-1)+(3x-5)(2x+7)=0

Solution for (2x+3)(x-1)+(3x-5)(2x+7)=0 equation:

Simplifying
(2x + 3)(x + -1) + (3x + -5)(2x + 7) = 0

Reorder the terms:
(3 + 2x)(x + -1) + (3x + -5)(2x + 7) = 0

Reorder the terms:
(3 + 2x)(-1 + x) + (3x + -5)(2x + 7) = 0

Multiply (3 + 2x) * (-1 + x)
(3(-1 + x) + 2x * (-1 + x)) + (3x + -5)(2x + 7) = 0
((-1 * 3 + x * 3) + 2x * (-1 + x)) + (3x + -5)(2x + 7) = 0
((-3 + 3x) + 2x * (-1 + x)) + (3x + -5)(2x + 7) = 0
(-3 + 3x + (-1 * 2x + x * 2x)) + (3x + -5)(2x + 7) = 0
(-3 + 3x + (-2x + 2x2)) + (3x + -5)(2x + 7) = 0

Combine like terms: 3x + -2x = 1x
(-3 + 1x + 2x2) + (3x + -5)(2x + 7) = 0

Reorder the terms:
-3 + 1x + 2x2 + (-5 + 3x)(2x + 7) = 0

Reorder the terms:
-3 + 1x + 2x2 + (-5 + 3x)(7 + 2x) = 0

Multiply (-5 + 3x) * (7 + 2x)
-3 + 1x + 2x2 + (-5(7 + 2x) + 3x * (7 + 2x)) = 0
-3 + 1x + 2x2 + ((7 * -5 + 2x * -5) + 3x * (7 + 2x)) = 0
-3 + 1x + 2x2 + ((-35 + -10x) + 3x * (7 + 2x)) = 0
-3 + 1x + 2x2 + (-35 + -10x + (7 * 3x + 2x * 3x)) = 0
-3 + 1x + 2x2 + (-35 + -10x + (21x + 6x2)) = 0

Combine like terms: -10x + 21x = 11x
-3 + 1x + 2x2 + (-35 + 11x + 6x2) = 0

Reorder the terms:
-3 + -35 + 1x + 11x + 2x2 + 6x2 = 0

Combine like terms: -3 + -35 = -38
-38 + 1x + 11x + 2x2 + 6x2 = 0

Combine like terms: 1x + 11x = 12x
-38 + 12x + 2x2 + 6x2 = 0

Combine like terms: 2x2 + 6x2 = 8x2
-38 + 12x + 8x2 = 0

Solving
-38 + 12x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + 6x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-19 + 6x + 4x2)' equal to zero and attempt to solve:

Simplifying
-19 + 6x + 4x2 = 0

Solving
-19 + 6x + 4x2 = 0

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

Divide each side by '4'.
-4.75 + 1.5x + x2 = 0

Move the constant term to the right:

Add '4.75' to each side of the equation.
-4.75 + 1.5x + 4.75 + x2 = 0 + 4.75

Reorder the terms:
-4.75 + 4.75 + 1.5x + x2 = 0 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + 1.5x + x2 = 0 + 4.75
1.5x + x2 = 0 + 4.75

Combine like terms: 0 + 4.75 = 4.75
1.5x + x2 = 4.75

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 4.75 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 4.75 + 0.5625

Combine like terms: 4.75 + 0.5625 = 5.3125
0.5625 + 1.5x + x2 = 5.3125

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 5.3125

Calculate the square root of the right side: 2.304886114

Break this problem into two subproblems by setting 
(x + 0.75) equal to 2.304886114 and -2.304886114.

Subproblem 1
x + 0.75 = 2.304886114

Simplifying
x + 0.75 = 2.304886114

Reorder the terms:
0.75 + x = 2.304886114

Solving
0.75 + x = 2.304886114

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 2.304886114 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 2.304886114 + -0.75
x = 2.304886114 + -0.75

Combine like terms: 2.304886114 + -0.75 = 1.554886114
x = 1.554886114

Simplifying
x = 1.554886114

Subproblem 2
x + 0.75 = -2.304886114

Simplifying
x + 0.75 = -2.304886114

Reorder the terms:
0.75 + x = -2.304886114

Solving
0.75 + x = -2.304886114

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -2.304886114 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -2.304886114 + -0.75
x = -2.304886114 + -0.75

Combine like terms: -2.304886114 + -0.75 = -3.054886114
x = -3.054886114

Simplifying
x = -3.054886114

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.554886114, -3.054886114}
Solution
x = {1.554886114, -3.054886114}