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

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

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

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

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

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

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

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

Combine like terms: 3x + -10x = -7x
-5 + 6x + 3x2 = -15 + -7x + 5x2

Solving
-5 + 6x + 3x2 = -15 + -7x + 5x2

Solving for variable 'x'.

Reorder the terms:
-5 + 15 + 6x + 7x + 3x2 + -5x2 = -15 + -7x + 5x2 + 15 + 7x + -5x2

Combine like terms: -5 + 15 = 10
10 + 6x + 7x + 3x2 + -5x2 = -15 + -7x + 5x2 + 15 + 7x + -5x2

Combine like terms: 6x + 7x = 13x
10 + 13x + 3x2 + -5x2 = -15 + -7x + 5x2 + 15 + 7x + -5x2

Combine like terms: 3x2 + -5x2 = -2x2
10 + 13x + -2x2 = -15 + -7x + 5x2 + 15 + 7x + -5x2

Reorder the terms:
10 + 13x + -2x2 = -15 + 15 + -7x + 7x + 5x2 + -5x2

Combine like terms: -15 + 15 = 0
10 + 13x + -2x2 = 0 + -7x + 7x + 5x2 + -5x2
10 + 13x + -2x2 = -7x + 7x + 5x2 + -5x2

Combine like terms: -7x + 7x = 0
10 + 13x + -2x2 = 0 + 5x2 + -5x2
10 + 13x + -2x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
10 + 13x + -2x2 = 0

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

Divide each side by '-2'.
-5 + -6.5x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -6.5x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -6.5x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6.5x + x2 = 0 + 5
-6.5x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-6.5x + x2 = 5

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 5 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 5 + 10.5625

Combine like terms: 5 + 10.5625 = 15.5625
10.5625 + -6.5x + x2 = 15.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 15.5625

Calculate the square root of the right side: 3.94493346

Break this problem into two subproblems by setting 
(x + -3.25) equal to 3.94493346 and -3.94493346.

Subproblem 1
x + -3.25 = 3.94493346

Simplifying
x + -3.25 = 3.94493346

Reorder the terms:
-3.25 + x = 3.94493346

Solving
-3.25 + x = 3.94493346

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 3.94493346 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 3.94493346 + 3.25
x = 3.94493346 + 3.25

Combine like terms: 3.94493346 + 3.25 = 7.19493346
x = 7.19493346

Simplifying
x = 7.19493346

Subproblem 2
x + -3.25 = -3.94493346

Simplifying
x + -3.25 = -3.94493346

Reorder the terms:
-3.25 + x = -3.94493346

Solving
-3.25 + x = -3.94493346

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -3.94493346 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -3.94493346 + 3.25
x = -3.94493346 + 3.25

Combine like terms: -3.94493346 + 3.25 = -0.69493346
x = -0.69493346

Simplifying
x = -0.69493346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.19493346, -0.69493346}