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 = -5x
1 + 9x = -15 + 3x2 + -1(6 + -5x + x2)
1 + 9x = -15 + 3x2 + (6 * -1 + -5x * -1 + x2 * -1)
1 + 9x = -15 + 3x2 + (-6 + 5x + -1x2)

Reorder the terms:
1 + 9x = -15 + -6 + 5x + 3x2 + -1x2

Combine like terms: -15 + -6 = -21
1 + 9x = -21 + 5x + 3x2 + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
1 + 9x = -21 + 5x + 2x2

Solving
1 + 9x = -21 + 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
1 + 21 + 9x + -5x + -2x2 = -21 + 5x + 2x2 + 21 + -5x + -2x2

Combine like terms: 1 + 21 = 22
22 + 9x + -5x + -2x2 = -21 + 5x + 2x2 + 21 + -5x + -2x2

Combine like terms: 9x + -5x = 4x
22 + 4x + -2x2 = -21 + 5x + 2x2 + 21 + -5x + -2x2

Reorder the terms:
22 + 4x + -2x2 = -21 + 21 + 5x + -5x + 2x2 + -2x2

Combine like terms: -21 + 21 = 0
22 + 4x + -2x2 = 0 + 5x + -5x + 2x2 + -2x2
22 + 4x + -2x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
22 + 4x + -2x2 = 0 + 2x2 + -2x2
22 + 4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
22 + 4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + 2x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(11 + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
11 + 2x + -1x2 = 0

Solving
11 + 2x + -1x2 = 0

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

Divide each side by '-1'.
-11 + -2x + x2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -2x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -2x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2x + x2 = 0 + 11
-2x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-2x + x2 = 11

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 11 + 1

Reorder the terms:
1 + -2x + x2 = 11 + 1

Combine like terms: 11 + 1 = 12
1 + -2x + x2 = 12

Factor a perfect square on the left side:
(x + -1)(x + -1) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + -1) equal to 3.464101615 and -3.464101615.

Subproblem 1
x + -1 = 3.464101615

Simplifying
x + -1 = 3.464101615

Reorder the terms:
-1 + x = 3.464101615

Solving
-1 + x = 3.464101615

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 3.464101615 + 1

Combine like terms: -1 + 1 = 0
0 + x = 3.464101615 + 1
x = 3.464101615 + 1

Combine like terms: 3.464101615 + 1 = 4.464101615
x = 4.464101615

Simplifying
x = 4.464101615

Subproblem 2
x + -1 = -3.464101615

Simplifying
x + -1 = -3.464101615

Reorder the terms:
-1 + x = -3.464101615

Solving
-1 + x = -3.464101615

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -3.464101615 + 1

Combine like terms: -1 + 1 = 0
0 + x = -3.464101615 + 1
x = -3.464101615 + 1

Combine like terms: -3.464101615 + 1 = -2.464101615
x = -2.464101615

Simplifying
x = -2.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.464101615, -2.464101615}
Solution
x = {4.464101615, -2.464101615}