(x+2)(3x+15)=20

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Solution for (x+2)(3x+15)=20 equation: 


Simplifying
(x + 2)(3x + 15) = 20

Reorder the terms:
(2 + x)(3x + 15) = 20

Reorder the terms:
(2 + x)(15 + 3x) = 20

Multiply (2 + x) * (15 + 3x)
(2(15 + 3x) + x(15 + 3x)) = 20
((15 * 2 + 3x * 2) + x(15 + 3x)) = 20
((30 + 6x) + x(15 + 3x)) = 20
(30 + 6x + (15 * x + 3x * x)) = 20
(30 + 6x + (15x + 3x2)) = 20

Combine like terms: 6x + 15x = 21x
(30 + 21x + 3x2) = 20

Solving
30 + 21x + 3x2 = 20

Solving for variable 'x'.

Reorder the terms:
30 + -20 + 21x + 3x2 = 20 + -20

Combine like terms: 30 + -20 = 10
10 + 21x + 3x2 = 20 + -20

Combine like terms: 20 + -20 = 0
10 + 21x + 3x2 = 0

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

Divide each side by '3'.
3.333333333 + 7x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + 7x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + 7x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + 7x + x2 = 0 + -3.333333333
7x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
7x + x2 = -3.333333333

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -3.333333333 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -3.333333333 + 12.25

Combine like terms: -3.333333333 + 12.25 = 8.916666667
12.25 + 7x + x2 = 8.916666667

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 8.916666667

Calculate the square root of the right side: 2.986078811

Break this problem into two subproblems by setting 
(x + 3.5) equal to 2.986078811 and -2.986078811.


Subproblem 1
x + 3.5 = 2.986078811

Simplifying
x + 3.5 = 2.986078811

Reorder the terms:
3.5 + x = 2.986078811

Solving
3.5 + x = 2.986078811

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 2.986078811 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 2.986078811 + -3.5
x = 2.986078811 + -3.5

Combine like terms: 2.986078811 + -3.5 = -0.513921189
x = -0.513921189

Simplifying
x = -0.513921189


Subproblem 2
x + 3.5 = -2.986078811

Simplifying
x + 3.5 = -2.986078811

Reorder the terms:
3.5 + x = -2.986078811

Solving
3.5 + x = -2.986078811

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -2.986078811 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -2.986078811 + -3.5
x = -2.986078811 + -3.5

Combine like terms: -2.986078811 + -3.5 = -6.486078811
x = -6.486078811

Simplifying
x = -6.486078811


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.513921189, -6.486078811}

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