3(x+1)(x+2)-(4-3x)(x+2)=36

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Solution for 3(x+1)(x+2)-(4-3x)(x+2)=36 equation: 


Simplifying
3(x + 1)(x + 2) + -1(4 + -3x)(x + 2) = 36

Reorder the terms:
3(1 + x)(x + 2) + -1(4 + -3x)(x + 2) = 36

Reorder the terms:
3(1 + x)(2 + x) + -1(4 + -3x)(x + 2) = 36

Multiply (1 + x) * (2 + x)
3(1(2 + x) + x(2 + x)) + -1(4 + -3x)(x + 2) = 36
3((2 * 1 + x * 1) + x(2 + x)) + -1(4 + -3x)(x + 2) = 36
3((2 + 1x) + x(2 + x)) + -1(4 + -3x)(x + 2) = 36
3(2 + 1x + (2 * x + x * x)) + -1(4 + -3x)(x + 2) = 36
3(2 + 1x + (2x + x2)) + -1(4 + -3x)(x + 2) = 36

Combine like terms: 1x + 2x = 3x
3(2 + 3x + x2) + -1(4 + -3x)(x + 2) = 36
(2 * 3 + 3x * 3 + x2 * 3) + -1(4 + -3x)(x + 2) = 36
(6 + 9x + 3x2) + -1(4 + -3x)(x + 2) = 36

Reorder the terms:
6 + 9x + 3x2 + -1(4 + -3x)(2 + x) = 36

Multiply (4 + -3x) * (2 + x)
6 + 9x + 3x2 + -1(4(2 + x) + -3x * (2 + x)) = 36
6 + 9x + 3x2 + -1((2 * 4 + x * 4) + -3x * (2 + x)) = 36
6 + 9x + 3x2 + -1((8 + 4x) + -3x * (2 + x)) = 36
6 + 9x + 3x2 + -1(8 + 4x + (2 * -3x + x * -3x)) = 36
6 + 9x + 3x2 + -1(8 + 4x + (-6x + -3x2)) = 36

Combine like terms: 4x + -6x = -2x
6 + 9x + 3x2 + -1(8 + -2x + -3x2) = 36
6 + 9x + 3x2 + (8 * -1 + -2x * -1 + -3x2 * -1) = 36
6 + 9x + 3x2 + (-8 + 2x + 3x2) = 36

Reorder the terms:
6 + -8 + 9x + 2x + 3x2 + 3x2 = 36

Combine like terms: 6 + -8 = -2
-2 + 9x + 2x + 3x2 + 3x2 = 36

Combine like terms: 9x + 2x = 11x
-2 + 11x + 3x2 + 3x2 = 36

Combine like terms: 3x2 + 3x2 = 6x2
-2 + 11x + 6x2 = 36

Solving
-2 + 11x + 6x2 = 36

Solving for variable 'x'.

Reorder the terms:
-2 + -36 + 11x + 6x2 = 36 + -36

Combine like terms: -2 + -36 = -38
-38 + 11x + 6x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-38 + 11x + 6x2 = 0

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

Divide each side by '6'.
-6.333333333 + 1.833333333x + x2 = 0

Move the constant term to the right:

Add '6.333333333' to each side of the equation.
-6.333333333 + 1.833333333x + 6.333333333 + x2 = 0 + 6.333333333

Reorder the terms:
-6.333333333 + 6.333333333 + 1.833333333x + x2 = 0 + 6.333333333

Combine like terms: -6.333333333 + 6.333333333 = 0.000000000
0.000000000 + 1.833333333x + x2 = 0 + 6.333333333
1.833333333x + x2 = 0 + 6.333333333

Combine like terms: 0 + 6.333333333 = 6.333333333
1.833333333x + x2 = 6.333333333

The x term is 1.833333333x.  Take half its coefficient (0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
1.833333333x + 0.8402777775 + x2 = 6.333333333 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333x + x2 = 6.333333333 + 0.8402777775

Combine like terms: 6.333333333 + 0.8402777775 = 7.1736111105
0.8402777775 + 1.833333333x + x2 = 7.1736111105

Factor a perfect square on the left side:
(x + 0.9166666665)(x + 0.9166666665) = 7.1736111105

Calculate the square root of the right side: 2.67835978

Break this problem into two subproblems by setting 
(x + 0.9166666665) equal to 2.67835978 and -2.67835978.


Subproblem 1
x + 0.9166666665 = 2.67835978

Simplifying
x + 0.9166666665 = 2.67835978

Reorder the terms:
0.9166666665 + x = 2.67835978

Solving
0.9166666665 + x = 2.67835978

Solving for variable 'x'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + x = 2.67835978 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + x = 2.67835978 + -0.9166666665
x = 2.67835978 + -0.9166666665

Combine like terms: 2.67835978 + -0.9166666665 = 1.7616931135
x = 1.7616931135

Simplifying
x = 1.7616931135


Subproblem 2
x + 0.9166666665 = -2.67835978

Simplifying
x + 0.9166666665 = -2.67835978

Reorder the terms:
0.9166666665 + x = -2.67835978

Solving
0.9166666665 + x = -2.67835978

Solving for variable 'x'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + x = -2.67835978 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + x = -2.67835978 + -0.9166666665
x = -2.67835978 + -0.9166666665

Combine like terms: -2.67835978 + -0.9166666665 = -3.5950264465
x = -3.5950264465

Simplifying
x = -3.5950264465


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.7616931135, -3.5950264465}

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