(x+2)(x+5)-(8x-3)(x+9)=

Solution for (x+2)(x+5)-(8x-3)(x+9)= equation:

Simplifying
(x + 2)(x + 5) + -1(8x + -3)(x + 9) = 0

Reorder the terms:
(2 + x)(x + 5) + -1(8x + -3)(x + 9) = 0

Reorder the terms:
(2 + x)(5 + x) + -1(8x + -3)(x + 9) = 0

Multiply (2 + x) * (5 + x)
(2(5 + x) + x(5 + x)) + -1(8x + -3)(x + 9) = 0
((5 * 2 + x * 2) + x(5 + x)) + -1(8x + -3)(x + 9) = 0
((10 + 2x) + x(5 + x)) + -1(8x + -3)(x + 9) = 0
(10 + 2x + (5 * x + x * x)) + -1(8x + -3)(x + 9) = 0
(10 + 2x + (5x + x2)) + -1(8x + -3)(x + 9) = 0

Combine like terms: 2x + 5x = 7x
(10 + 7x + x2) + -1(8x + -3)(x + 9) = 0

Reorder the terms:
10 + 7x + x2 + -1(-3 + 8x)(x + 9) = 0

Reorder the terms:
10 + 7x + x2 + -1(-3 + 8x)(9 + x) = 0

Multiply (-3 + 8x) * (9 + x)
10 + 7x + x2 + -1(-3(9 + x) + 8x * (9 + x)) = 0
10 + 7x + x2 + -1((9 * -3 + x * -3) + 8x * (9 + x)) = 0
10 + 7x + x2 + -1((-27 + -3x) + 8x * (9 + x)) = 0
10 + 7x + x2 + -1(-27 + -3x + (9 * 8x + x * 8x)) = 0
10 + 7x + x2 + -1(-27 + -3x + (72x + 8x2)) = 0

Combine like terms: -3x + 72x = 69x
10 + 7x + x2 + -1(-27 + 69x + 8x2) = 0
10 + 7x + x2 + (-27 * -1 + 69x * -1 + 8x2 * -1) = 0
10 + 7x + x2 + (27 + -69x + -8x2) = 0

Reorder the terms:
10 + 27 + 7x + -69x + x2 + -8x2 = 0

Combine like terms: 10 + 27 = 37
37 + 7x + -69x + x2 + -8x2 = 0

Combine like terms: 7x + -69x = -62x
37 + -62x + x2 + -8x2 = 0

Combine like terms: x2 + -8x2 = -7x2
37 + -62x + -7x2 = 0

Solving
37 + -62x + -7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-5.285714286 + 8.857142857x + x2 = 0

Move the constant term to the right:

Add '5.285714286' to each side of the equation.
-5.285714286 + 8.857142857x + 5.285714286 + x2 = 0 + 5.285714286

Reorder the terms:
-5.285714286 + 5.285714286 + 8.857142857x + x2 = 0 + 5.285714286

Combine like terms: -5.285714286 + 5.285714286 = 0.000000000
0.000000000 + 8.857142857x + x2 = 0 + 5.285714286
8.857142857x + x2 = 0 + 5.285714286

Combine like terms: 0 + 5.285714286 = 5.285714286
8.857142857x + x2 = 5.285714286

The x term is 8.857142857x.  Take half its coefficient (4.428571429).
Square it (19.61224490) and add it to both sides.

Add '19.61224490' to each side of the equation.
8.857142857x + 19.61224490 + x2 = 5.285714286 + 19.61224490

Reorder the terms:
19.61224490 + 8.857142857x + x2 = 5.285714286 + 19.61224490

Combine like terms: 5.285714286 + 19.61224490 = 24.897959186
19.61224490 + 8.857142857x + x2 = 24.897959186

Factor a perfect square on the left side:
(x + 4.428571429)(x + 4.428571429) = 24.897959186

Calculate the square root of the right side: 4.989785485

Break this problem into two subproblems by setting 
(x + 4.428571429) equal to 4.989785485 and -4.989785485.

Subproblem 1
x + 4.428571429 = 4.989785485

Simplifying
x + 4.428571429 = 4.989785485

Reorder the terms:
4.428571429 + x = 4.989785485

Solving
4.428571429 + x = 4.989785485

Solving for variable 'x'.

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

Add '-4.428571429' to each side of the equation.
4.428571429 + -4.428571429 + x = 4.989785485 + -4.428571429

Combine like terms: 4.428571429 + -4.428571429 = 0.000000000
0.000000000 + x = 4.989785485 + -4.428571429
x = 4.989785485 + -4.428571429

Combine like terms: 4.989785485 + -4.428571429 = 0.561214056
x = 0.561214056

Simplifying
x = 0.561214056

Subproblem 2
x + 4.428571429 = -4.989785485

Simplifying
x + 4.428571429 = -4.989785485

Reorder the terms:
4.428571429 + x = -4.989785485

Solving
4.428571429 + x = -4.989785485

Solving for variable 'x'.

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

Add '-4.428571429' to each side of the equation.
4.428571429 + -4.428571429 + x = -4.989785485 + -4.428571429

Combine like terms: 4.428571429 + -4.428571429 = 0.000000000
0.000000000 + x = -4.989785485 + -4.428571429
x = -4.989785485 + -4.428571429

Combine like terms: -4.989785485 + -4.428571429 = -9.418356914
x = -9.418356914

Simplifying
x = -9.418356914

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.561214056, -9.418356914}