8x(x-1)+(3x+5)(5x-1)=3((3x+5)(x+1))

Solution for 8x(x-1)+(3x+5)(5x-1)=3((3x+5)(x+1)) equation:

Simplifying
8x(x + -1) + (3x + 5)(5x + -1) = 3((3x + 5)(x + 1))

Reorder the terms:
8x(-1 + x) + (3x + 5)(5x + -1) = 3((3x + 5)(x + 1))
(-1 * 8x + x * 8x) + (3x + 5)(5x + -1) = 3((3x + 5)(x + 1))
(-8x + 8x2) + (3x + 5)(5x + -1) = 3((3x + 5)(x + 1))

Reorder the terms:
-8x + 8x2 + (5 + 3x)(5x + -1) = 3((3x + 5)(x + 1))

Reorder the terms:
-8x + 8x2 + (5 + 3x)(-1 + 5x) = 3((3x + 5)(x + 1))

Multiply (5 + 3x) * (-1 + 5x)
-8x + 8x2 + (5(-1 + 5x) + 3x * (-1 + 5x)) = 3((3x + 5)(x + 1))
-8x + 8x2 + ((-1 * 5 + 5x * 5) + 3x * (-1 + 5x)) = 3((3x + 5)(x + 1))
-8x + 8x2 + ((-5 + 25x) + 3x * (-1 + 5x)) = 3((3x + 5)(x + 1))
-8x + 8x2 + (-5 + 25x + (-1 * 3x + 5x * 3x)) = 3((3x + 5)(x + 1))
-8x + 8x2 + (-5 + 25x + (-3x + 15x2)) = 3((3x + 5)(x + 1))

Combine like terms: 25x + -3x = 22x
-8x + 8x2 + (-5 + 22x + 15x2) = 3((3x + 5)(x + 1))

Reorder the terms:
-5 + -8x + 22x + 8x2 + 15x2 = 3((3x + 5)(x + 1))

Combine like terms: -8x + 22x = 14x
-5 + 14x + 8x2 + 15x2 = 3((3x + 5)(x + 1))

Combine like terms: 8x2 + 15x2 = 23x2
-5 + 14x + 23x2 = 3((3x + 5)(x + 1))

Reorder the terms:
-5 + 14x + 23x2 = 3((5 + 3x)(x + 1))

Reorder the terms:
-5 + 14x + 23x2 = 3((5 + 3x)(1 + x))

Multiply (5 + 3x) * (1 + x)
-5 + 14x + 23x2 = 3((5(1 + x) + 3x * (1 + x)))
-5 + 14x + 23x2 = 3(((1 * 5 + x * 5) + 3x * (1 + x)))
-5 + 14x + 23x2 = 3(((5 + 5x) + 3x * (1 + x)))
-5 + 14x + 23x2 = 3((5 + 5x + (1 * 3x + x * 3x)))
-5 + 14x + 23x2 = 3((5 + 5x + (3x + 3x2)))

Combine like terms: 5x + 3x = 8x
-5 + 14x + 23x2 = 3((5 + 8x + 3x2))
-5 + 14x + 23x2 = (5 * 3 + 8x * 3 + 3x2 * 3)
-5 + 14x + 23x2 = (15 + 24x + 9x2)

Solving
-5 + 14x + 23x2 = 15 + 24x + 9x2

Solving for variable 'x'.

Reorder the terms:
-5 + -15 + 14x + -24x + 23x2 + -9x2 = 15 + 24x + 9x2 + -15 + -24x + -9x2

Combine like terms: -5 + -15 = -20
-20 + 14x + -24x + 23x2 + -9x2 = 15 + 24x + 9x2 + -15 + -24x + -9x2

Combine like terms: 14x + -24x = -10x
-20 + -10x + 23x2 + -9x2 = 15 + 24x + 9x2 + -15 + -24x + -9x2

Combine like terms: 23x2 + -9x2 = 14x2
-20 + -10x + 14x2 = 15 + 24x + 9x2 + -15 + -24x + -9x2

Reorder the terms:
-20 + -10x + 14x2 = 15 + -15 + 24x + -24x + 9x2 + -9x2

Combine like terms: 15 + -15 = 0
-20 + -10x + 14x2 = 0 + 24x + -24x + 9x2 + -9x2
-20 + -10x + 14x2 = 24x + -24x + 9x2 + -9x2

Combine like terms: 24x + -24x = 0
-20 + -10x + 14x2 = 0 + 9x2 + -9x2
-20 + -10x + 14x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-20 + -10x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -5x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + -5x + 7x2)' equal to zero and attempt to solve:

Simplifying
-10 + -5x + 7x2 = 0

Solving
-10 + -5x + 7x2 = 0

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

Divide each side by '7'.
-1.428571429 + -0.7142857143x + x2 = 0

Move the constant term to the right:

Add '1.428571429' to each side of the equation.
-1.428571429 + -0.7142857143x + 1.428571429 + x2 = 0 + 1.428571429

Reorder the terms:
-1.428571429 + 1.428571429 + -0.7142857143x + x2 = 0 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + -0.7142857143x + x2 = 0 + 1.428571429
-0.7142857143x + x2 = 0 + 1.428571429

Combine like terms: 0 + 1.428571429 = 1.428571429
-0.7142857143x + x2 = 1.428571429

The x term is -0.7142857143x.  Take half its coefficient (-0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
-0.7142857143x + 0.1275510204 + x2 = 1.428571429 + 0.1275510204

Reorder the terms:
0.1275510204 + -0.7142857143x + x2 = 1.428571429 + 0.1275510204

Combine like terms: 1.428571429 + 0.1275510204 = 1.5561224494
0.1275510204 + -0.7142857143x + x2 = 1.5561224494

Factor a perfect square on the left side:
(x + -0.3571428572)(x + -0.3571428572) = 1.5561224494

Calculate the square root of the right side: 1.247446371

Break this problem into two subproblems by setting 
(x + -0.3571428572) equal to 1.247446371 and -1.247446371.

Subproblem 1
x + -0.3571428572 = 1.247446371

Simplifying
x + -0.3571428572 = 1.247446371

Reorder the terms:
-0.3571428572 + x = 1.247446371

Solving
-0.3571428572 + x = 1.247446371

Solving for variable 'x'.

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

Add '0.3571428572' to each side of the equation.
-0.3571428572 + 0.3571428572 + x = 1.247446371 + 0.3571428572

Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000
0.0000000000 + x = 1.247446371 + 0.3571428572
x = 1.247446371 + 0.3571428572

Combine like terms: 1.247446371 + 0.3571428572 = 1.6045892282
x = 1.6045892282

Simplifying
x = 1.6045892282

Subproblem 2
x + -0.3571428572 = -1.247446371

Simplifying
x + -0.3571428572 = -1.247446371

Reorder the terms:
-0.3571428572 + x = -1.247446371

Solving
-0.3571428572 + x = -1.247446371

Solving for variable 'x'.

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

Add '0.3571428572' to each side of the equation.
-0.3571428572 + 0.3571428572 + x = -1.247446371 + 0.3571428572

Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000
0.0000000000 + x = -1.247446371 + 0.3571428572
x = -1.247446371 + 0.3571428572

Combine like terms: -1.247446371 + 0.3571428572 = -0.8903035138
x = -0.8903035138

Simplifying
x = -0.8903035138

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.6045892282, -0.8903035138}
Solution
x = {1.6045892282, -0.8903035138}