6(2x-3+4)(x+1)=6x+36

Solution for 6(2x-3+4)(x+1)=6x+36 equation:

Simplifying
6(2x + -3 + 4)(x + 1) = 6x + 36

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

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

Reorder the terms:
6(1 + 2x)(1 + x) = 6x + 36

Multiply (1 + 2x) * (1 + x)
6(1(1 + x) + 2x * (1 + x)) = 6x + 36
6((1 * 1 + x * 1) + 2x * (1 + x)) = 6x + 36
6((1 + 1x) + 2x * (1 + x)) = 6x + 36
6(1 + 1x + (1 * 2x + x * 2x)) = 6x + 36
6(1 + 1x + (2x + 2x2)) = 6x + 36

Combine like terms: 1x + 2x = 3x
6(1 + 3x + 2x2) = 6x + 36
(1 * 6 + 3x * 6 + 2x2 * 6) = 6x + 36
(6 + 18x + 12x2) = 6x + 36

Reorder the terms:
6 + 18x + 12x2 = 36 + 6x

Solving
6 + 18x + 12x2 = 36 + 6x

Solving for variable 'x'.

Reorder the terms:
6 + -36 + 18x + -6x + 12x2 = 36 + 6x + -36 + -6x

Combine like terms: 6 + -36 = -30
-30 + 18x + -6x + 12x2 = 36 + 6x + -36 + -6x

Combine like terms: 18x + -6x = 12x
-30 + 12x + 12x2 = 36 + 6x + -36 + -6x

Reorder the terms:
-30 + 12x + 12x2 = 36 + -36 + 6x + -6x

Combine like terms: 36 + -36 = 0
-30 + 12x + 12x2 = 0 + 6x + -6x
-30 + 12x + 12x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-30 + 12x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-5 + 2x + 2x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-5 + 2x + 2x2)' equal to zero and attempt to solve:

Simplifying
-5 + 2x + 2x2 = 0

Solving
-5 + 2x + 2x2 = 0

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

Divide each side by '2'.
-2.5 + x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x + x2 = 0 + 2.5
x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
x + x2 = 2.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 2.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 2.5 + 0.25

Combine like terms: 2.5 + 0.25 = 2.75
1.25 + x2 = 2.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.658312395 and -1.658312395.

Subproblem 1
x + 0.5 = 1.658312395

Simplifying
x + 0.5 = 1.658312395

Reorder the terms:
0.5 + x = 1.658312395

Solving
0.5 + x = 1.658312395

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.658312395 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.658312395 + -0.5
x = 1.658312395 + -0.5

Combine like terms: 1.658312395 + -0.5 = 1.158312395
x = 1.158312395

Simplifying
x = 1.158312395

Subproblem 2
x + 0.5 = -1.658312395

Simplifying
x + 0.5 = -1.658312395

Reorder the terms:
0.5 + x = -1.658312395

Solving
0.5 + x = -1.658312395

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.658312395 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.658312395 + -0.5
x = -1.658312395 + -0.5

Combine like terms: -1.658312395 + -0.5 = -2.158312395
x = -2.158312395

Simplifying
x = -2.158312395

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.158312395, -2.158312395}
Solution
x = {1.158312395, -2.158312395}