=(-9x^2+3)-(x+1)

Solution for =(-9x^2+3)-(x+1) equation:

Simplifying
0 = (-9x2 + 3) + -1(x + 1)

Reorder the terms:
0 = (3 + -9x2) + -1(x + 1)

Remove parenthesis around (3 + -9x2)
0 = 3 + -9x2 + -1(x + 1)

Reorder the terms:
0 = 3 + -9x2 + -1(1 + x)
0 = 3 + -9x2 + (1 * -1 + x * -1)
0 = 3 + -9x2 + (-1 + -1x)

Reorder the terms:
0 = 3 + -1 + -1x + -9x2

Combine like terms: 3 + -1 = 2
0 = 2 + -1x + -9x2

Solving
0 = 2 + -1x + -9x2

Solving for variable 'x'.

Combine like terms: 0 + -2 = -2
-2 + x + 9x2 = 2 + -1x + -9x2 + -2 + x + 9x2

Reorder the terms:
-2 + x + 9x2 = 2 + -2 + -1x + x + -9x2 + 9x2

Combine like terms: 2 + -2 = 0
-2 + x + 9x2 = 0 + -1x + x + -9x2 + 9x2
-2 + x + 9x2 = -1x + x + -9x2 + 9x2

Combine like terms: -1x + x = 0
-2 + x + 9x2 = 0 + -9x2 + 9x2
-2 + x + 9x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-2 + x + 9x2 = 0

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

Divide each side by '9'.
-0.2222222222 + 0.1111111111x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.1111111111x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + 0.1111111111x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + 0.1111111111x + x2 = 0 + 0.2222222222
0.1111111111x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
0.1111111111x + x2 = 0.2222222222

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.
0.1111111111x + 0.25 + x2 = 0.2222222222 + 0.25

Reorder the terms:
0.25 + 0.1111111111x + x2 = 0.2222222222 + 0.25

Combine like terms: 0.2222222222 + 0.25 = 0.4722222222
0.25 + 0.1111111111x + x2 = 0.4722222222

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.4722222222

Calculate the square root of the right side: 0.687184271

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.687184271 and -0.687184271.

Subproblem 1
x + 0.5 = 0.687184271

Simplifying
x + 0.5 = 0.687184271

Reorder the terms:
0.5 + x = 0.687184271

Solving
0.5 + x = 0.687184271

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 = 0.687184271 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.687184271 + -0.5
x = 0.687184271 + -0.5

Combine like terms: 0.687184271 + -0.5 = 0.187184271
x = 0.187184271

Simplifying
x = 0.187184271

Subproblem 2
x + 0.5 = -0.687184271

Simplifying
x + 0.5 = -0.687184271

Reorder the terms:
0.5 + x = -0.687184271

Solving
0.5 + x = -0.687184271

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 = -0.687184271 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.687184271 + -0.5
x = -0.687184271 + -0.5

Combine like terms: -0.687184271 + -0.5 = -1.187184271
x = -1.187184271

Simplifying
x = -1.187184271

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.187184271, -1.187184271}