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

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

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

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

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

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

Solving
6x + 2x2 = 3 + -1x

Solving for variable 'x'.

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

Combine like terms: 6x + x = 7x
-3 + 7x + 2x2 = 3 + -1x + -3 + x

Reorder the terms:
-3 + 7x + 2x2 = 3 + -3 + -1x + x

Combine like terms: 3 + -3 = 0
-3 + 7x + 2x2 = 0 + -1x + x
-3 + 7x + 2x2 = -1x + x

Combine like terms: -1x + x = 0
-3 + 7x + 2x2 = 0

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

Divide each side by '2'.
-1.5 + 3.5x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 3.5x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 3.5x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 3.5x + x2 = 0 + 1.5
3.5x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
3.5x + x2 = 1.5

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 1.5 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 1.5 + 3.0625

Combine like terms: 1.5 + 3.0625 = 4.5625
3.0625 + 3.5x + x2 = 4.5625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(x + 1.75) equal to 2.136000936 and -2.136000936.

Subproblem 1
x + 1.75 = 2.136000936

Simplifying
x + 1.75 = 2.136000936

Reorder the terms:
1.75 + x = 2.136000936

Solving
1.75 + x = 2.136000936

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 2.136000936 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 2.136000936 + -1.75
x = 2.136000936 + -1.75

Combine like terms: 2.136000936 + -1.75 = 0.386000936
x = 0.386000936

Simplifying
x = 0.386000936

Subproblem 2
x + 1.75 = -2.136000936

Simplifying
x + 1.75 = -2.136000936

Reorder the terms:
1.75 + x = -2.136000936

Solving
1.75 + x = -2.136000936

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -2.136000936 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -2.136000936 + -1.75
x = -2.136000936 + -1.75

Combine like terms: -2.136000936 + -1.75 = -3.886000936
x = -3.886000936

Simplifying
x = -3.886000936

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.386000936, -3.886000936}