(5x+1)(x+3)(-8)=5(x+1)(x+2)

Solution for (5x+1)(x+3)(-8)=5(x+1)(x+2) equation:

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

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

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

Reorder the terms for easier multiplication:
-8(1 + 5x)(3 + x) = 5(x + 1)(x + 2)

Multiply (1 + 5x) * (3 + x)
-8(1(3 + x) + 5x * (3 + x)) = 5(x + 1)(x + 2)
-8((3 * 1 + x * 1) + 5x * (3 + x)) = 5(x + 1)(x + 2)
-8((3 + 1x) + 5x * (3 + x)) = 5(x + 1)(x + 2)
-8(3 + 1x + (3 * 5x + x * 5x)) = 5(x + 1)(x + 2)
-8(3 + 1x + (15x + 5x2)) = 5(x + 1)(x + 2)

Combine like terms: 1x + 15x = 16x
-8(3 + 16x + 5x2) = 5(x + 1)(x + 2)
(3 * -8 + 16x * -8 + 5x2 * -8) = 5(x + 1)(x + 2)
(-24 + -128x + -40x2) = 5(x + 1)(x + 2)

Reorder the terms:
-24 + -128x + -40x2 = 5(1 + x)(x + 2)

Reorder the terms:
-24 + -128x + -40x2 = 5(1 + x)(2 + x)

Multiply (1 + x) * (2 + x)
-24 + -128x + -40x2 = 5(1(2 + x) + x(2 + x))
-24 + -128x + -40x2 = 5((2 * 1 + x * 1) + x(2 + x))
-24 + -128x + -40x2 = 5((2 + 1x) + x(2 + x))
-24 + -128x + -40x2 = 5(2 + 1x + (2 * x + x * x))
-24 + -128x + -40x2 = 5(2 + 1x + (2x + x2))

Combine like terms: 1x + 2x = 3x
-24 + -128x + -40x2 = 5(2 + 3x + x2)
-24 + -128x + -40x2 = (2 * 5 + 3x * 5 + x2 * 5)
-24 + -128x + -40x2 = (10 + 15x + 5x2)

Solving
-24 + -128x + -40x2 = 10 + 15x + 5x2

Solving for variable 'x'.

Reorder the terms:
-24 + -10 + -128x + -15x + -40x2 + -5x2 = 10 + 15x + 5x2 + -10 + -15x + -5x2

Combine like terms: -24 + -10 = -34
-34 + -128x + -15x + -40x2 + -5x2 = 10 + 15x + 5x2 + -10 + -15x + -5x2

Combine like terms: -128x + -15x = -143x
-34 + -143x + -40x2 + -5x2 = 10 + 15x + 5x2 + -10 + -15x + -5x2

Combine like terms: -40x2 + -5x2 = -45x2
-34 + -143x + -45x2 = 10 + 15x + 5x2 + -10 + -15x + -5x2

Reorder the terms:
-34 + -143x + -45x2 = 10 + -10 + 15x + -15x + 5x2 + -5x2

Combine like terms: 10 + -10 = 0
-34 + -143x + -45x2 = 0 + 15x + -15x + 5x2 + -5x2
-34 + -143x + -45x2 = 15x + -15x + 5x2 + -5x2

Combine like terms: 15x + -15x = 0
-34 + -143x + -45x2 = 0 + 5x2 + -5x2
-34 + -143x + -45x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-34 + -143x + -45x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(34 + 143x + 45x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(34 + 143x + 45x2)' equal to zero and attempt to solve:

Simplifying
34 + 143x + 45x2 = 0

Solving
34 + 143x + 45x2 = 0

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

Divide each side by '45'.
0.7555555556 + 3.177777778x + x2 = 0

Move the constant term to the right:

Add '-0.7555555556' to each side of the equation.
0.7555555556 + 3.177777778x + -0.7555555556 + x2 = 0 + -0.7555555556

Reorder the terms:
0.7555555556 + -0.7555555556 + 3.177777778x + x2 = 0 + -0.7555555556

Combine like terms: 0.7555555556 + -0.7555555556 = 0.0000000000
0.0000000000 + 3.177777778x + x2 = 0 + -0.7555555556
3.177777778x + x2 = 0 + -0.7555555556

Combine like terms: 0 + -0.7555555556 = -0.7555555556
3.177777778x + x2 = -0.7555555556

The x term is 3.177777778x.  Take half its coefficient (1.588888889).
Square it (2.524567902) and add it to both sides.

Add '2.524567902' to each side of the equation.
3.177777778x + 2.524567902 + x2 = -0.7555555556 + 2.524567902

Reorder the terms:
2.524567902 + 3.177777778x + x2 = -0.7555555556 + 2.524567902

Combine like terms: -0.7555555556 + 2.524567902 = 1.7690123464
2.524567902 + 3.177777778x + x2 = 1.7690123464

Factor a perfect square on the left side:
(x + 1.588888889)(x + 1.588888889) = 1.7690123464

Calculate the square root of the right side: 1.330042235

Break this problem into two subproblems by setting 
(x + 1.588888889) equal to 1.330042235 and -1.330042235.

Subproblem 1
x + 1.588888889 = 1.330042235

Simplifying
x + 1.588888889 = 1.330042235

Reorder the terms:
1.588888889 + x = 1.330042235

Solving
1.588888889 + x = 1.330042235

Solving for variable 'x'.

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

Add '-1.588888889' to each side of the equation.
1.588888889 + -1.588888889 + x = 1.330042235 + -1.588888889

Combine like terms: 1.588888889 + -1.588888889 = 0.000000000
0.000000000 + x = 1.330042235 + -1.588888889
x = 1.330042235 + -1.588888889

Combine like terms: 1.330042235 + -1.588888889 = -0.258846654
x = -0.258846654

Simplifying
x = -0.258846654

Subproblem 2
x + 1.588888889 = -1.330042235

Simplifying
x + 1.588888889 = -1.330042235

Reorder the terms:
1.588888889 + x = -1.330042235

Solving
1.588888889 + x = -1.330042235

Solving for variable 'x'.

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

Add '-1.588888889' to each side of the equation.
1.588888889 + -1.588888889 + x = -1.330042235 + -1.588888889

Combine like terms: 1.588888889 + -1.588888889 = 0.000000000
0.000000000 + x = -1.330042235 + -1.588888889
x = -1.330042235 + -1.588888889

Combine like terms: -1.330042235 + -1.588888889 = -2.918931124
x = -2.918931124

Simplifying
x = -2.918931124

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.258846654, -2.918931124}
Solution
x = {-0.258846654, -2.918931124}