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

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

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

Remove parenthesis around (3x)
3x(5)(-1x + -3)(2) = (x + 2)(3)

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

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

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

Multiply 15 * 2
30x(-3 + -1x) = (x + 2)(3)
(-3 * 30x + -1x * 30x) = (x + 2)(3)
(-90x + -30x2) = (x + 2)(3)

Reorder the terms:
-90x + -30x2 = (2 + x)(3)

Reorder the terms for easier multiplication:
-90x + -30x2 = 3(2 + x)
-90x + -30x2 = (2 * 3 + x * 3)
-90x + -30x2 = (6 + 3x)

Solving
-90x + -30x2 = 6 + 3x

Solving for variable 'x'.

Reorder the terms:
-6 + -90x + -3x + -30x2 = 6 + 3x + -6 + -3x

Combine like terms: -90x + -3x = -93x
-6 + -93x + -30x2 = 6 + 3x + -6 + -3x

Reorder the terms:
-6 + -93x + -30x2 = 6 + -6 + 3x + -3x

Combine like terms: 6 + -6 = 0
-6 + -93x + -30x2 = 0 + 3x + -3x
-6 + -93x + -30x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-6 + -93x + -30x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(2 + 31x + 10x2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(2 + 31x + 10x2)' equal to zero and attempt to solve:

Simplifying
2 + 31x + 10x2 = 0

Solving
2 + 31x + 10x2 = 0

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

Divide each side by '10'.
0.2 + 3.1x + x2 = 0.0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 3.1x + -0.2 + x2 = 0.0 + -0.2

Reorder the terms:
0.2 + -0.2 + 3.1x + x2 = 0.0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 3.1x + x2 = 0.0 + -0.2
3.1x + x2 = 0.0 + -0.2

Combine like terms: 0.0 + -0.2 = -0.2
3.1x + x2 = -0.2

The x term is 3.1x.  Take half its coefficient (1.55).
Square it (2.4025) and add it to both sides.

Add '2.4025' to each side of the equation.
3.1x + 2.4025 + x2 = -0.2 + 2.4025

Reorder the terms:
2.4025 + 3.1x + x2 = -0.2 + 2.4025

Combine like terms: -0.2 + 2.4025 = 2.2025
2.4025 + 3.1x + x2 = 2.2025

Factor a perfect square on the left side:
(x + 1.55)(x + 1.55) = 2.2025

Calculate the square root of the right side: 1.484082208

Break this problem into two subproblems by setting 
(x + 1.55) equal to 1.484082208 and -1.484082208.

Subproblem 1
x + 1.55 = 1.484082208

Simplifying
x + 1.55 = 1.484082208

Reorder the terms:
1.55 + x = 1.484082208

Solving
1.55 + x = 1.484082208

Solving for variable 'x'.

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

Add '-1.55' to each side of the equation.
1.55 + -1.55 + x = 1.484082208 + -1.55

Combine like terms: 1.55 + -1.55 = 0.00
0.00 + x = 1.484082208 + -1.55
x = 1.484082208 + -1.55

Combine like terms: 1.484082208 + -1.55 = -0.065917792
x = -0.065917792

Simplifying
x = -0.065917792

Subproblem 2
x + 1.55 = -1.484082208

Simplifying
x + 1.55 = -1.484082208

Reorder the terms:
1.55 + x = -1.484082208

Solving
1.55 + x = -1.484082208

Solving for variable 'x'.

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

Add '-1.55' to each side of the equation.
1.55 + -1.55 + x = -1.484082208 + -1.55

Combine like terms: 1.55 + -1.55 = 0.00
0.00 + x = -1.484082208 + -1.55
x = -1.484082208 + -1.55

Combine like terms: -1.484082208 + -1.55 = -3.034082208
x = -3.034082208

Simplifying
x = -3.034082208

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.065917792, -3.034082208}
Solution
x = {-0.065917792, -3.034082208}