3(x+4)=(x+5)(x-6)

Solution for 3(x+4)=(x+5)(x-6) equation:

Simplifying
3(x + 4) = (x + 5)(x + -6)

Reorder the terms:
3(4 + x) = (x + 5)(x + -6)
(4 * 3 + x * 3) = (x + 5)(x + -6)
(12 + 3x) = (x + 5)(x + -6)

Reorder the terms:
12 + 3x = (5 + x)(x + -6)

Reorder the terms:
12 + 3x = (5 + x)(-6 + x)

Multiply (5 + x) * (-6 + x)
12 + 3x = (5(-6 + x) + x(-6 + x))
12 + 3x = ((-6 * 5 + x * 5) + x(-6 + x))
12 + 3x = ((-30 + 5x) + x(-6 + x))
12 + 3x = (-30 + 5x + (-6 * x + x * x))
12 + 3x = (-30 + 5x + (-6x + x2))

Combine like terms: 5x + -6x = -1x
12 + 3x = (-30 + -1x + x2)

Solving
12 + 3x = -30 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
12 + 30 + 3x + x + -1x2 = -30 + -1x + x2 + 30 + x + -1x2

Combine like terms: 12 + 30 = 42
42 + 3x + x + -1x2 = -30 + -1x + x2 + 30 + x + -1x2

Combine like terms: 3x + x = 4x
42 + 4x + -1x2 = -30 + -1x + x2 + 30 + x + -1x2

Reorder the terms:
42 + 4x + -1x2 = -30 + 30 + -1x + x + x2 + -1x2

Combine like terms: -30 + 30 = 0
42 + 4x + -1x2 = 0 + -1x + x + x2 + -1x2
42 + 4x + -1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
42 + 4x + -1x2 = 0 + x2 + -1x2
42 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
42 + 4x + -1x2 = 0

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

Divide each side by '-1'.
-42 + -4x + x2 = 0

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + -4x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + -4x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -4x + x2 = 0 + 42
-4x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
-4x + x2 = 42

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 42 + 4

Reorder the terms:
4 + -4x + x2 = 42 + 4

Combine like terms: 42 + 4 = 46
4 + -4x + x2 = 46

Factor a perfect square on the left side:
(x + -2)(x + -2) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x + -2) equal to 6.782329983 and -6.782329983.

Subproblem 1
x + -2 = 6.782329983

Simplifying
x + -2 = 6.782329983

Reorder the terms:
-2 + x = 6.782329983

Solving
-2 + x = 6.782329983

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 6.782329983 + 2

Combine like terms: -2 + 2 = 0
0 + x = 6.782329983 + 2
x = 6.782329983 + 2

Combine like terms: 6.782329983 + 2 = 8.782329983
x = 8.782329983

Simplifying
x = 8.782329983

Subproblem 2
x + -2 = -6.782329983

Simplifying
x + -2 = -6.782329983

Reorder the terms:
-2 + x = -6.782329983

Solving
-2 + x = -6.782329983

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -6.782329983 + 2

Combine like terms: -2 + 2 = 0
0 + x = -6.782329983 + 2
x = -6.782329983 + 2

Combine like terms: -6.782329983 + 2 = -4.782329983
x = -4.782329983

Simplifying
x = -4.782329983

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.782329983, -4.782329983}