(x+5)(2x+1)-(x-3)(x-5)=(x-3)(-(10x+14))

Solution for (x+5)(2x+1)-(x-3)(x-5)=(x-3)(-(10x+14)) equation:

Simplifying
(x + 5)(2x + 1) + -1(x + -3)(x + -5) = (x + -3)(-1(10x + 14))

Reorder the terms:
(5 + x)(2x + 1) + -1(x + -3)(x + -5) = (x + -3)(-1(10x + 14))

Reorder the terms:
(5 + x)(1 + 2x) + -1(x + -3)(x + -5) = (x + -3)(-1(10x + 14))

Multiply (5 + x) * (1 + 2x)
(5(1 + 2x) + x(1 + 2x)) + -1(x + -3)(x + -5) = (x + -3)(-1(10x + 14))
((1 * 5 + 2x * 5) + x(1 + 2x)) + -1(x + -3)(x + -5) = (x + -3)(-1(10x + 14))
((5 + 10x) + x(1 + 2x)) + -1(x + -3)(x + -5) = (x + -3)(-1(10x + 14))
(5 + 10x + (1 * x + 2x * x)) + -1(x + -3)(x + -5) = (x + -3)(-1(10x + 14))
(5 + 10x + (1x + 2x2)) + -1(x + -3)(x + -5) = (x + -3)(-1(10x + 14))

Combine like terms: 10x + 1x = 11x
(5 + 11x + 2x2) + -1(x + -3)(x + -5) = (x + -3)(-1(10x + 14))

Reorder the terms:
5 + 11x + 2x2 + -1(-3 + x)(x + -5) = (x + -3)(-1(10x + 14))

Reorder the terms:
5 + 11x + 2x2 + -1(-3 + x)(-5 + x) = (x + -3)(-1(10x + 14))

Multiply (-3 + x) * (-5 + x)
5 + 11x + 2x2 + -1(-3(-5 + x) + x(-5 + x)) = (x + -3)(-1(10x + 14))
5 + 11x + 2x2 + -1((-5 * -3 + x * -3) + x(-5 + x)) = (x + -3)(-1(10x + 14))
5 + 11x + 2x2 + -1((15 + -3x) + x(-5 + x)) = (x + -3)(-1(10x + 14))
5 + 11x + 2x2 + -1(15 + -3x + (-5 * x + x * x)) = (x + -3)(-1(10x + 14))
5 + 11x + 2x2 + -1(15 + -3x + (-5x + x2)) = (x + -3)(-1(10x + 14))

Combine like terms: -3x + -5x = -8x
5 + 11x + 2x2 + -1(15 + -8x + x2) = (x + -3)(-1(10x + 14))
5 + 11x + 2x2 + (15 * -1 + -8x * -1 + x2 * -1) = (x + -3)(-1(10x + 14))
5 + 11x + 2x2 + (-15 + 8x + -1x2) = (x + -3)(-1(10x + 14))

Reorder the terms:
5 + -15 + 11x + 8x + 2x2 + -1x2 = (x + -3)(-1(10x + 14))

Combine like terms: 5 + -15 = -10
-10 + 11x + 8x + 2x2 + -1x2 = (x + -3)(-1(10x + 14))

Combine like terms: 11x + 8x = 19x
-10 + 19x + 2x2 + -1x2 = (x + -3)(-1(10x + 14))

Combine like terms: 2x2 + -1x2 = 1x2
-10 + 19x + 1x2 = (x + -3)(-1(10x + 14))

Reorder the terms:
-10 + 19x + 1x2 = (-3 + x)(-1(10x + 14))

Reorder the terms:
-10 + 19x + 1x2 = (-3 + x)(-1(14 + 10x))
-10 + 19x + 1x2 = (-3 + x)((14 * -1 + 10x * -1))
-10 + 19x + 1x2 = (-3 + x)((-14 + -10x))

Multiply (-3 + x) * (-14 + -10x)
-10 + 19x + 1x2 = (-3(-14 + -10x) + x(-14 + -10x))
-10 + 19x + 1x2 = ((-14 * -3 + -10x * -3) + x(-14 + -10x))
-10 + 19x + 1x2 = ((42 + 30x) + x(-14 + -10x))
-10 + 19x + 1x2 = (42 + 30x + (-14 * x + -10x * x))
-10 + 19x + 1x2 = (42 + 30x + (-14x + -10x2))

Combine like terms: 30x + -14x = 16x
-10 + 19x + 1x2 = (42 + 16x + -10x2)

Solving
-10 + 19x + 1x2 = 42 + 16x + -10x2

Solving for variable 'x'.

Reorder the terms:
-10 + -42 + 19x + -16x + 1x2 + 10x2 = 42 + 16x + -10x2 + -42 + -16x + 10x2

Combine like terms: -10 + -42 = -52
-52 + 19x + -16x + 1x2 + 10x2 = 42 + 16x + -10x2 + -42 + -16x + 10x2

Combine like terms: 19x + -16x = 3x
-52 + 3x + 1x2 + 10x2 = 42 + 16x + -10x2 + -42 + -16x + 10x2

Combine like terms: 1x2 + 10x2 = 11x2
-52 + 3x + 11x2 = 42 + 16x + -10x2 + -42 + -16x + 10x2

Reorder the terms:
-52 + 3x + 11x2 = 42 + -42 + 16x + -16x + -10x2 + 10x2

Combine like terms: 42 + -42 = 0
-52 + 3x + 11x2 = 0 + 16x + -16x + -10x2 + 10x2
-52 + 3x + 11x2 = 16x + -16x + -10x2 + 10x2

Combine like terms: 16x + -16x = 0
-52 + 3x + 11x2 = 0 + -10x2 + 10x2
-52 + 3x + 11x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
-52 + 3x + 11x2 = 0

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

Divide each side by '11'.
-4.727272727 + 0.2727272727x + x2 = 0

Move the constant term to the right:

Add '4.727272727' to each side of the equation.
-4.727272727 + 0.2727272727x + 4.727272727 + x2 = 0 + 4.727272727

Reorder the terms:
-4.727272727 + 4.727272727 + 0.2727272727x + x2 = 0 + 4.727272727

Combine like terms: -4.727272727 + 4.727272727 = 0.000000000
0.000000000 + 0.2727272727x + x2 = 0 + 4.727272727
0.2727272727x + x2 = 0 + 4.727272727

Combine like terms: 0 + 4.727272727 = 4.727272727
0.2727272727x + x2 = 4.727272727

The x term is 0.2727272727x.  Take half its coefficient (0.1363636364).
Square it (0.01859504133) and add it to both sides.

Add '0.01859504133' to each side of the equation.
0.2727272727x + 0.01859504133 + x2 = 4.727272727 + 0.01859504133

Reorder the terms:
0.01859504133 + 0.2727272727x + x2 = 4.727272727 + 0.01859504133

Combine like terms: 4.727272727 + 0.01859504133 = 4.74586776833
0.01859504133 + 0.2727272727x + x2 = 4.74586776833

Factor a perfect square on the left side:
(x + 0.1363636364)(x + 0.1363636364) = 4.74586776833

Calculate the square root of the right side: 2.178501267

Break this problem into two subproblems by setting 
(x + 0.1363636364) equal to 2.178501267 and -2.178501267.

Subproblem 1
x + 0.1363636364 = 2.178501267

Simplifying
x + 0.1363636364 = 2.178501267

Reorder the terms:
0.1363636364 + x = 2.178501267

Solving
0.1363636364 + x = 2.178501267

Solving for variable 'x'.

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

Add '-0.1363636364' to each side of the equation.
0.1363636364 + -0.1363636364 + x = 2.178501267 + -0.1363636364

Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000
0.0000000000 + x = 2.178501267 + -0.1363636364
x = 2.178501267 + -0.1363636364

Combine like terms: 2.178501267 + -0.1363636364 = 2.0421376306
x = 2.0421376306

Simplifying
x = 2.0421376306

Subproblem 2
x + 0.1363636364 = -2.178501267

Simplifying
x + 0.1363636364 = -2.178501267

Reorder the terms:
0.1363636364 + x = -2.178501267

Solving
0.1363636364 + x = -2.178501267

Solving for variable 'x'.

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

Add '-0.1363636364' to each side of the equation.
0.1363636364 + -0.1363636364 + x = -2.178501267 + -0.1363636364

Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000
0.0000000000 + x = -2.178501267 + -0.1363636364
x = -2.178501267 + -0.1363636364

Combine like terms: -2.178501267 + -0.1363636364 = -2.3148649034
x = -2.3148649034

Simplifying
x = -2.3148649034

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.0421376306, -2.3148649034}