(2x^2-4x+8)+(-3x^2+15x-12)=

Solution for (2x^2-4x+8)+(-3x^2+15x-12)= equation:

Simplifying
(2x2 + -4x + 8) + (-3x2 + 15x + -12) = 0

Reorder the terms:
(8 + -4x + 2x2) + (-3x2 + 15x + -12) = 0

Remove parenthesis around (8 + -4x + 2x2)
8 + -4x + 2x2 + (-3x2 + 15x + -12) = 0

Reorder the terms:
8 + -4x + 2x2 + (-12 + 15x + -3x2) = 0

Remove parenthesis around (-12 + 15x + -3x2)
8 + -4x + 2x2 + -12 + 15x + -3x2 = 0

Reorder the terms:
8 + -12 + -4x + 15x + 2x2 + -3x2 = 0

Combine like terms: 8 + -12 = -4
-4 + -4x + 15x + 2x2 + -3x2 = 0

Combine like terms: -4x + 15x = 11x
-4 + 11x + 2x2 + -3x2 = 0

Combine like terms: 2x2 + -3x2 = -1x2
-4 + 11x + -1x2 = 0

Solving
-4 + 11x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
4 + -11x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -11x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -11x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -11x + x2 = 0 + -4
-11x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-11x + x2 = -4

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -4 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -4 + 30.25

Combine like terms: -4 + 30.25 = 26.25
30.25 + -11x + x2 = 26.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(x + -5.5) equal to 5.123475383 and -5.123475383.

Subproblem 1
x + -5.5 = 5.123475383

Simplifying
x + -5.5 = 5.123475383

Reorder the terms:
-5.5 + x = 5.123475383

Solving
-5.5 + x = 5.123475383

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 5.123475383 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 5.123475383 + 5.5
x = 5.123475383 + 5.5

Combine like terms: 5.123475383 + 5.5 = 10.623475383
x = 10.623475383

Simplifying
x = 10.623475383

Subproblem 2
x + -5.5 = -5.123475383

Simplifying
x + -5.5 = -5.123475383

Reorder the terms:
-5.5 + x = -5.123475383

Solving
-5.5 + x = -5.123475383

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -5.123475383 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -5.123475383 + 5.5
x = -5.123475383 + 5.5

Combine like terms: -5.123475383 + 5.5 = 0.376524617
x = 0.376524617

Simplifying
x = 0.376524617

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.623475383, 0.376524617}