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

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

Simplifying
x(x + 1) = 3x + 3(2x + -3) + -1x + 1(2x)

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

Reorder the terms:
1x + x2 = 3x + 3(-3 + 2x) + -1x + 1(2x)
1x + x2 = 3x + (-3 * 3 + 2x * 3) + -1x + 1(2x)
1x + x2 = 3x + (-9 + 6x) + -1x + 1(2x)

Remove parenthesis around (2x)
1x + x2 = 3x + -9 + 6x + -1x + 1 * 2x

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

Reorder the terms:
1x + x2 = -9 + 3x + 6x + -1x + 2x

Combine like terms: 3x + 6x = 9x
1x + x2 = -9 + 9x + -1x + 2x

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

Combine like terms: 8x + 2x = 10x
1x + x2 = -9 + 10x

Solving
1x + x2 = -9 + 10x

Solving for variable 'x'.

Reorder the terms:
9 + 1x + -10x + x2 = -9 + 10x + 9 + -10x

Combine like terms: 1x + -10x = -9x
9 + -9x + x2 = -9 + 10x + 9 + -10x

Reorder the terms:
9 + -9x + x2 = -9 + 9 + 10x + -10x

Combine like terms: -9 + 9 = 0
9 + -9x + x2 = 0 + 10x + -10x
9 + -9x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
9 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -9x + -9 + x2 = 0 + -9

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

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

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

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -9 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -9 + 20.25

Combine like terms: -9 + 20.25 = 11.25
20.25 + -9x + x2 = 11.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.354101966 and -3.354101966.

Subproblem 1
x + -4.5 = 3.354101966

Simplifying
x + -4.5 = 3.354101966

Reorder the terms:
-4.5 + x = 3.354101966

Solving
-4.5 + x = 3.354101966

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 3.354101966 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 3.354101966 + 4.5
x = 3.354101966 + 4.5

Combine like terms: 3.354101966 + 4.5 = 7.854101966
x = 7.854101966

Simplifying
x = 7.854101966

Subproblem 2
x + -4.5 = -3.354101966

Simplifying
x + -4.5 = -3.354101966

Reorder the terms:
-4.5 + x = -3.354101966

Solving
-4.5 + x = -3.354101966

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -3.354101966 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -3.354101966 + 4.5
x = -3.354101966 + 4.5

Combine like terms: -3.354101966 + 4.5 = 1.145898034
x = 1.145898034

Simplifying
x = 1.145898034

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.854101966, 1.145898034}