46=x+(2x-5)(3x+6)

Solution for 46=x+(2x-5)(3x+6) equation:

Simplifying
46 = x + (2x + -5)(3x + 6)

Reorder the terms:
46 = x + (-5 + 2x)(3x + 6)

Reorder the terms:
46 = x + (-5 + 2x)(6 + 3x)

Multiply (-5 + 2x) * (6 + 3x)
46 = x + (-5(6 + 3x) + 2x * (6 + 3x))
46 = x + ((6 * -5 + 3x * -5) + 2x * (6 + 3x))
46 = x + ((-30 + -15x) + 2x * (6 + 3x))
46 = x + (-30 + -15x + (6 * 2x + 3x * 2x))
46 = x + (-30 + -15x + (12x + 6x2))

Combine like terms: -15x + 12x = -3x
46 = x + (-30 + -3x + 6x2)

Reorder the terms:
46 = -30 + x + -3x + 6x2

Combine like terms: x + -3x = -2x
46 = -30 + -2x + 6x2

Solving
46 = -30 + -2x + 6x2

Solving for variable 'x'.

Combine like terms: 46 + 30 = 76
76 + 2x + -6x2 = -30 + -2x + 6x2 + 30 + 2x + -6x2

Reorder the terms:
76 + 2x + -6x2 = -30 + 30 + -2x + 2x + 6x2 + -6x2

Combine like terms: -30 + 30 = 0
76 + 2x + -6x2 = 0 + -2x + 2x + 6x2 + -6x2
76 + 2x + -6x2 = -2x + 2x + 6x2 + -6x2

Combine like terms: -2x + 2x = 0
76 + 2x + -6x2 = 0 + 6x2 + -6x2
76 + 2x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
76 + 2x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(38 + x + -3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(38 + x + -3x2)' equal to zero and attempt to solve:

Simplifying
38 + x + -3x2 = 0

Solving
38 + x + -3x2 = 0

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

Divide each side by '-3'.
-12.66666667 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '12.66666667' to each side of the equation.
-12.66666667 + -0.3333333333x + 12.66666667 + x2 = 0 + 12.66666667

Reorder the terms:
-12.66666667 + 12.66666667 + -0.3333333333x + x2 = 0 + 12.66666667

Combine like terms: -12.66666667 + 12.66666667 = 0.00000000
0.00000000 + -0.3333333333x + x2 = 0 + 12.66666667
-0.3333333333x + x2 = 0 + 12.66666667

Combine like terms: 0 + 12.66666667 = 12.66666667
-0.3333333333x + x2 = 12.66666667

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.
-0.3333333333x + 0.25 + x2 = 12.66666667 + 0.25

Reorder the terms:
0.25 + -0.3333333333x + x2 = 12.66666667 + 0.25

Combine like terms: 12.66666667 + 0.25 = 12.91666667
0.25 + -0.3333333333x + x2 = 12.91666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 12.91666667

Calculate the square root of the right side: 3.593976443

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.593976443 and -3.593976443.

Subproblem 1
x + 0.5 = 3.593976443

Simplifying
x + 0.5 = 3.593976443

Reorder the terms:
0.5 + x = 3.593976443

Solving
0.5 + x = 3.593976443

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 = 3.593976443 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.593976443 + -0.5
x = 3.593976443 + -0.5

Combine like terms: 3.593976443 + -0.5 = 3.093976443
x = 3.093976443

Simplifying
x = 3.093976443

Subproblem 2
x + 0.5 = -3.593976443

Simplifying
x + 0.5 = -3.593976443

Reorder the terms:
0.5 + x = -3.593976443

Solving
0.5 + x = -3.593976443

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 = -3.593976443 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.593976443 + -0.5
x = -3.593976443 + -0.5

Combine like terms: -3.593976443 + -0.5 = -4.093976443
x = -4.093976443

Simplifying
x = -4.093976443

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.093976443, -4.093976443}
Solution
x = {3.093976443, -4.093976443}