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

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

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

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

Remove parenthesis around (2x + x2)
3(2x + x2 + -2) + 1 = 3(x2 + 2x) + -5(3 + -1(x2 + 2x))

Reorder the terms:
3(-2 + 2x + x2) + 1 = 3(x2 + 2x) + -5(3 + -1(x2 + 2x))
(-2 * 3 + 2x * 3 + x2 * 3) + 1 = 3(x2 + 2x) + -5(3 + -1(x2 + 2x))
(-6 + 6x + 3x2) + 1 = 3(x2 + 2x) + -5(3 + -1(x2 + 2x))

Reorder the terms:
-6 + 1 + 6x + 3x2 = 3(x2 + 2x) + -5(3 + -1(x2 + 2x))

Combine like terms: -6 + 1 = -5
-5 + 6x + 3x2 = 3(x2 + 2x) + -5(3 + -1(x2 + 2x))

Reorder the terms:
-5 + 6x + 3x2 = 3(2x + x2) + -5(3 + -1(x2 + 2x))
-5 + 6x + 3x2 = (2x * 3 + x2 * 3) + -5(3 + -1(x2 + 2x))
-5 + 6x + 3x2 = (6x + 3x2) + -5(3 + -1(x2 + 2x))

Reorder the terms:
-5 + 6x + 3x2 = 6x + 3x2 + -5(3 + -1(2x + x2))
-5 + 6x + 3x2 = 6x + 3x2 + -5(3 + (2x * -1 + x2 * -1))
-5 + 6x + 3x2 = 6x + 3x2 + -5(3 + (-2x + -1x2))
-5 + 6x + 3x2 = 6x + 3x2 + (3 * -5 + -2x * -5 + -1x2 * -5)
-5 + 6x + 3x2 = 6x + 3x2 + (-15 + 10x + 5x2)

Reorder the terms:
-5 + 6x + 3x2 = -15 + 6x + 10x + 3x2 + 5x2

Combine like terms: 6x + 10x = 16x
-5 + 6x + 3x2 = -15 + 16x + 3x2 + 5x2

Combine like terms: 3x2 + 5x2 = 8x2
-5 + 6x + 3x2 = -15 + 16x + 8x2

Solving
-5 + 6x + 3x2 = -15 + 16x + 8x2

Solving for variable 'x'.

Reorder the terms:
-5 + 15 + 6x + -16x + 3x2 + -8x2 = -15 + 16x + 8x2 + 15 + -16x + -8x2

Combine like terms: -5 + 15 = 10
10 + 6x + -16x + 3x2 + -8x2 = -15 + 16x + 8x2 + 15 + -16x + -8x2

Combine like terms: 6x + -16x = -10x
10 + -10x + 3x2 + -8x2 = -15 + 16x + 8x2 + 15 + -16x + -8x2

Combine like terms: 3x2 + -8x2 = -5x2
10 + -10x + -5x2 = -15 + 16x + 8x2 + 15 + -16x + -8x2

Reorder the terms:
10 + -10x + -5x2 = -15 + 15 + 16x + -16x + 8x2 + -8x2

Combine like terms: -15 + 15 = 0
10 + -10x + -5x2 = 0 + 16x + -16x + 8x2 + -8x2
10 + -10x + -5x2 = 16x + -16x + 8x2 + -8x2

Combine like terms: 16x + -16x = 0
10 + -10x + -5x2 = 0 + 8x2 + -8x2
10 + -10x + -5x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
10 + -10x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + -2x + -1x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(2 + -2x + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -2x + -1x2 = 0

Solving
2 + -2x + -1x2 = 0

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

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

Move the constant term to the right:

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

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

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

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

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 = 2 + 1

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

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

Factor a perfect square on the left side:
(x + 1)(x + 1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + 1) equal to 1.732050808 and -1.732050808.

Subproblem 1
x + 1 = 1.732050808

Simplifying
x + 1 = 1.732050808

Reorder the terms:
1 + x = 1.732050808

Solving
1 + x = 1.732050808

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 = 1.732050808 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.732050808 + -1
x = 1.732050808 + -1

Combine like terms: 1.732050808 + -1 = 0.732050808
x = 0.732050808

Simplifying
x = 0.732050808

Subproblem 2
x + 1 = -1.732050808

Simplifying
x + 1 = -1.732050808

Reorder the terms:
1 + x = -1.732050808

Solving
1 + x = -1.732050808

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 = -1.732050808 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.732050808 + -1
x = -1.732050808 + -1

Combine like terms: -1.732050808 + -1 = -2.732050808
x = -2.732050808

Simplifying
x = -2.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.732050808, -2.732050808}
Solution
x = {0.732050808, -2.732050808}