x(x+3)+234=(2x+3)(x-1)

Solution for x(x+3)+234=(2x+3)(x-1) equation:

Simplifying
x(x + 3) + 234 = (2x + 3)(x + -1)

Reorder the terms:
x(3 + x) + 234 = (2x + 3)(x + -1)
(3 * x + x * x) + 234 = (2x + 3)(x + -1)
(3x + x2) + 234 = (2x + 3)(x + -1)

Reorder the terms:
234 + 3x + x2 = (2x + 3)(x + -1)

Reorder the terms:
234 + 3x + x2 = (3 + 2x)(x + -1)

Reorder the terms:
234 + 3x + x2 = (3 + 2x)(-1 + x)

Multiply (3 + 2x) * (-1 + x)
234 + 3x + x2 = (3(-1 + x) + 2x * (-1 + x))
234 + 3x + x2 = ((-1 * 3 + x * 3) + 2x * (-1 + x))
234 + 3x + x2 = ((-3 + 3x) + 2x * (-1 + x))
234 + 3x + x2 = (-3 + 3x + (-1 * 2x + x * 2x))
234 + 3x + x2 = (-3 + 3x + (-2x + 2x2))

Combine like terms: 3x + -2x = 1x
234 + 3x + x2 = (-3 + 1x + 2x2)

Solving
234 + 3x + x2 = -3 + 1x + 2x2

Solving for variable 'x'.

Reorder the terms:
234 + 3 + 3x + -1x + x2 + -2x2 = -3 + 1x + 2x2 + 3 + -1x + -2x2

Combine like terms: 234 + 3 = 237
237 + 3x + -1x + x2 + -2x2 = -3 + 1x + 2x2 + 3 + -1x + -2x2

Combine like terms: 3x + -1x = 2x
237 + 2x + x2 + -2x2 = -3 + 1x + 2x2 + 3 + -1x + -2x2

Combine like terms: x2 + -2x2 = -1x2
237 + 2x + -1x2 = -3 + 1x + 2x2 + 3 + -1x + -2x2

Reorder the terms:
237 + 2x + -1x2 = -3 + 3 + 1x + -1x + 2x2 + -2x2

Combine like terms: -3 + 3 = 0
237 + 2x + -1x2 = 0 + 1x + -1x + 2x2 + -2x2
237 + 2x + -1x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
237 + 2x + -1x2 = 0 + 2x2 + -2x2
237 + 2x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
237 + 2x + -1x2 = 0

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

Divide each side by '-1'.
-237 + -2x + x2 = 0

Move the constant term to the right:

Add '237' to each side of the equation.
-237 + -2x + 237 + x2 = 0 + 237

Reorder the terms:
-237 + 237 + -2x + x2 = 0 + 237

Combine like terms: -237 + 237 = 0
0 + -2x + x2 = 0 + 237
-2x + x2 = 0 + 237

Combine like terms: 0 + 237 = 237
-2x + x2 = 237

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 = 237 + 1

Reorder the terms:
1 + -2x + x2 = 237 + 1

Combine like terms: 237 + 1 = 238
1 + -2x + x2 = 238

Factor a perfect square on the left side:
(x + -1)(x + -1) = 238

Calculate the square root of the right side: 15.427248621

Break this problem into two subproblems by setting 
(x + -1) equal to 15.427248621 and -15.427248621.

Subproblem 1
x + -1 = 15.427248621

Simplifying
x + -1 = 15.427248621

Reorder the terms:
-1 + x = 15.427248621

Solving
-1 + x = 15.427248621

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 = 15.427248621 + 1

Combine like terms: -1 + 1 = 0
0 + x = 15.427248621 + 1
x = 15.427248621 + 1

Combine like terms: 15.427248621 + 1 = 16.427248621
x = 16.427248621

Simplifying
x = 16.427248621

Subproblem 2
x + -1 = -15.427248621

Simplifying
x + -1 = -15.427248621

Reorder the terms:
-1 + x = -15.427248621

Solving
-1 + x = -15.427248621

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 = -15.427248621 + 1

Combine like terms: -1 + 1 = 0
0 + x = -15.427248621 + 1
x = -15.427248621 + 1

Combine like terms: -15.427248621 + 1 = -14.427248621
x = -14.427248621

Simplifying
x = -14.427248621

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.427248621, -14.427248621}