((3x+1)-(x^2-6))(x)=

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

Simplifying
((3x + 1) + -1(x2 + -6))(x) = 0

Reorder the terms:
((1 + 3x) + -1(x2 + -6))(x) = 0

Remove parenthesis around (1 + 3x)
(1 + 3x + -1(x2 + -6))(x) = 0

Reorder the terms:
(1 + 3x + -1(-6 + x2))(x) = 0
(1 + 3x + (-6 * -1 + x2 * -1))(x) = 0
(1 + 3x + (6 + -1x2))(x) = 0

Reorder the terms:
(1 + 6 + 3x + -1x2)(x) = 0

Combine like terms: 1 + 6 = 7
(7 + 3x + -1x2)(x) = 0

Reorder the terms for easier multiplication:
x(7 + 3x + -1x2) = 0
(7 * x + 3x * x + -1x2 * x) = 0
(7x + 3x2 + -1x3) = 0

Solving
7x + 3x2 + -1x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + 3x + -1x2) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(7 + 3x + -1x2)' equal to zero and attempt to solve:

Simplifying
7 + 3x + -1x2 = 0

Solving
7 + 3x + -1x2 = 0

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

Divide each side by '-1'.
-7 + -3x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -3x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -3x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x + x2 = 0 + 7
-3x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-3x + x2 = 7

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 7 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 7 + 2.25

Combine like terms: 7 + 2.25 = 9.25
2.25 + -3x + x2 = 9.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.041381265 and -3.041381265.

Subproblem 1
x + -1.5 = 3.041381265

Simplifying
x + -1.5 = 3.041381265

Reorder the terms:
-1.5 + x = 3.041381265

Solving
-1.5 + x = 3.041381265

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 3.041381265 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 3.041381265 + 1.5
x = 3.041381265 + 1.5

Combine like terms: 3.041381265 + 1.5 = 4.541381265
x = 4.541381265

Simplifying
x = 4.541381265

Subproblem 2
x + -1.5 = -3.041381265

Simplifying
x + -1.5 = -3.041381265

Reorder the terms:
-1.5 + x = -3.041381265

Solving
-1.5 + x = -3.041381265

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -3.041381265 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -3.041381265 + 1.5
x = -3.041381265 + 1.5

Combine like terms: -3.041381265 + 1.5 = -1.541381265
x = -1.541381265

Simplifying
x = -1.541381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.541381265, -1.541381265}
Solution
x = {0, 4.541381265, -1.541381265}