79=(x+(x+1))(x+2)-(x+3)

Solution for 79=(x+(x+1))(x+2)-(x+3) equation:

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

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

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

Reorder the terms:
79 = (1 + x + x)(x + 2) + -1(x + 3)

Combine like terms: x + x = 2x
79 = (1 + 2x)(x + 2) + -1(x + 3)

Reorder the terms:
79 = (1 + 2x)(2 + x) + -1(x + 3)

Multiply (1 + 2x) * (2 + x)
79 = (1(2 + x) + 2x * (2 + x)) + -1(x + 3)
79 = ((2 * 1 + x * 1) + 2x * (2 + x)) + -1(x + 3)
79 = ((2 + 1x) + 2x * (2 + x)) + -1(x + 3)
79 = (2 + 1x + (2 * 2x + x * 2x)) + -1(x + 3)
79 = (2 + 1x + (4x + 2x2)) + -1(x + 3)

Combine like terms: 1x + 4x = 5x
79 = (2 + 5x + 2x2) + -1(x + 3)

Reorder the terms:
79 = 2 + 5x + 2x2 + -1(3 + x)
79 = 2 + 5x + 2x2 + (3 * -1 + x * -1)
79 = 2 + 5x + 2x2 + (-3 + -1x)

Reorder the terms:
79 = 2 + -3 + 5x + -1x + 2x2

Combine like terms: 2 + -3 = -1
79 = -1 + 5x + -1x + 2x2

Combine like terms: 5x + -1x = 4x
79 = -1 + 4x + 2x2

Solving
79 = -1 + 4x + 2x2

Solving for variable 'x'.

Combine like terms: 79 + 1 = 80
80 + -4x + -2x2 = -1 + 4x + 2x2 + 1 + -4x + -2x2

Reorder the terms:
80 + -4x + -2x2 = -1 + 1 + 4x + -4x + 2x2 + -2x2

Combine like terms: -1 + 1 = 0
80 + -4x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2
80 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
80 + -4x + -2x2 = 0 + 2x2 + -2x2
80 + -4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
80 + -4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + -2x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(40 + -2x + -1x2)' equal to zero and attempt to solve:

Simplifying
40 + -2x + -1x2 = 0

Solving
40 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-40 + 2x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 2x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 2x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 2x + x2 = 0 + 40
2x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
2x + x2 = 40

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 40 + 1

Reorder the terms:
1 + 2x + x2 = 40 + 1

Combine like terms: 40 + 1 = 41
1 + 2x + x2 = 41

Factor a perfect square on the left side:
(x + 1)(x + 1) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + 1) equal to 6.403124237 and -6.403124237.

Subproblem 1
x + 1 = 6.403124237

Simplifying
x + 1 = 6.403124237

Reorder the terms:
1 + x = 6.403124237

Solving
1 + x = 6.403124237

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 6.403124237 + -1

Combine like terms: 1 + -1 = 0
0 + x = 6.403124237 + -1
x = 6.403124237 + -1

Combine like terms: 6.403124237 + -1 = 5.403124237
x = 5.403124237

Simplifying
x = 5.403124237

Subproblem 2
x + 1 = -6.403124237

Simplifying
x + 1 = -6.403124237

Reorder the terms:
1 + x = -6.403124237

Solving
1 + x = -6.403124237

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -6.403124237 + -1

Combine like terms: 1 + -1 = 0
0 + x = -6.403124237 + -1
x = -6.403124237 + -1

Combine like terms: -6.403124237 + -1 = -7.403124237
x = -7.403124237

Simplifying
x = -7.403124237

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.403124237, -7.403124237}
Solution
x = {5.403124237, -7.403124237}