9x-1=3(x^2-5)-(x-3)(x+2)

Solution for 9x-1=3(x^2-5)-(x-3)(x+2) equation:

Simplifying
9x + -1 = 3(x2 + -5) + -1(x + -3)(x + 2)

Reorder the terms:
-1 + 9x = 3(x2 + -5) + -1(x + -3)(x + 2)

Reorder the terms:
-1 + 9x = 3(-5 + x2) + -1(x + -3)(x + 2)
-1 + 9x = (-5 * 3 + x2 * 3) + -1(x + -3)(x + 2)
-1 + 9x = (-15 + 3x2) + -1(x + -3)(x + 2)

Reorder the terms:
-1 + 9x = -15 + 3x2 + -1(-3 + x)(x + 2)

Reorder the terms:
-1 + 9x = -15 + 3x2 + -1(-3 + x)(2 + x)

Multiply (-3 + x) * (2 + x)
-1 + 9x = -15 + 3x2 + -1(-3(2 + x) + x(2 + x))
-1 + 9x = -15 + 3x2 + -1((2 * -3 + x * -3) + x(2 + x))
-1 + 9x = -15 + 3x2 + -1((-6 + -3x) + x(2 + x))
-1 + 9x = -15 + 3x2 + -1(-6 + -3x + (2 * x + x * x))
-1 + 9x = -15 + 3x2 + -1(-6 + -3x + (2x + x2))

Combine like terms: -3x + 2x = -1x
-1 + 9x = -15 + 3x2 + -1(-6 + -1x + x2)
-1 + 9x = -15 + 3x2 + (-6 * -1 + -1x * -1 + x2 * -1)
-1 + 9x = -15 + 3x2 + (6 + 1x + -1x2)

Reorder the terms:
-1 + 9x = -15 + 6 + 1x + 3x2 + -1x2

Combine like terms: -15 + 6 = -9
-1 + 9x = -9 + 1x + 3x2 + -1x2

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

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

Solving for variable 'x'.

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

Combine like terms: -1 + 9 = 8
8 + 9x + -1x + -2x2 = -9 + 1x + 2x2 + 9 + -1x + -2x2

Combine like terms: 9x + -1x = 8x
8 + 8x + -2x2 = -9 + 1x + 2x2 + 9 + -1x + -2x2

Reorder the terms:
8 + 8x + -2x2 = -9 + 9 + 1x + -1x + 2x2 + -2x2

Combine like terms: -9 + 9 = 0
8 + 8x + -2x2 = 0 + 1x + -1x + 2x2 + -2x2
8 + 8x + -2x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
8 + 8x + -2x2 = 0 + 2x2 + -2x2
8 + 8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
8 + 8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 4x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + 4x + -1x2)' equal to zero and attempt to solve:

Simplifying
4 + 4x + -1x2 = 0

Solving
4 + 4x + -1x2 = 0

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

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

Move the constant term to the right:

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

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

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

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

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 = 4 + 4

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

Combine like terms: 4 + 4 = 8
4 + -4x + x2 = 8

Factor a perfect square on the left side:
(x + -2)(x + -2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -2) equal to 2.828427125 and -2.828427125.

Subproblem 1
x + -2 = 2.828427125

Simplifying
x + -2 = 2.828427125

Reorder the terms:
-2 + x = 2.828427125

Solving
-2 + x = 2.828427125

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 = 2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.828427125 + 2
x = 2.828427125 + 2

Combine like terms: 2.828427125 + 2 = 4.828427125
x = 4.828427125

Simplifying
x = 4.828427125

Subproblem 2
x + -2 = -2.828427125

Simplifying
x + -2 = -2.828427125

Reorder the terms:
-2 + x = -2.828427125

Solving
-2 + x = -2.828427125

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 = -2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.828427125 + 2
x = -2.828427125 + 2

Combine like terms: -2.828427125 + 2 = -0.828427125
x = -0.828427125

Simplifying
x = -0.828427125

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.828427125, -0.828427125}
Solution
x = {4.828427125, -0.828427125}