8(3-x)+2=4x(x+x-1)-18

Solution for 8(3-x)+2=4x(x+x-1)-18 equation:

Simplifying
8(3 + -1x) + 2 = 4x(x + x + -1) + -18
(3 * 8 + -1x * 8) + 2 = 4x(x + x + -1) + -18
(24 + -8x) + 2 = 4x(x + x + -1) + -18

Reorder the terms:
24 + 2 + -8x = 4x(x + x + -1) + -18

Combine like terms: 24 + 2 = 26
26 + -8x = 4x(x + x + -1) + -18

Reorder the terms:
26 + -8x = 4x(-1 + x + x) + -18

Combine like terms: x + x = 2x
26 + -8x = 4x(-1 + 2x) + -18
26 + -8x = (-1 * 4x + 2x * 4x) + -18
26 + -8x = (-4x + 8x2) + -18

Reorder the terms:
26 + -8x = -18 + -4x + 8x2

Solving
26 + -8x = -18 + -4x + 8x2

Solving for variable 'x'.

Reorder the terms:
26 + 18 + -8x + 4x + -8x2 = -18 + -4x + 8x2 + 18 + 4x + -8x2

Combine like terms: 26 + 18 = 44
44 + -8x + 4x + -8x2 = -18 + -4x + 8x2 + 18 + 4x + -8x2

Combine like terms: -8x + 4x = -4x
44 + -4x + -8x2 = -18 + -4x + 8x2 + 18 + 4x + -8x2

Reorder the terms:
44 + -4x + -8x2 = -18 + 18 + -4x + 4x + 8x2 + -8x2

Combine like terms: -18 + 18 = 0
44 + -4x + -8x2 = 0 + -4x + 4x + 8x2 + -8x2
44 + -4x + -8x2 = -4x + 4x + 8x2 + -8x2

Combine like terms: -4x + 4x = 0
44 + -4x + -8x2 = 0 + 8x2 + -8x2
44 + -4x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
44 + -4x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(11 + -1x + -2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(11 + -1x + -2x2)' equal to zero and attempt to solve:

Simplifying
11 + -1x + -2x2 = 0

Solving
11 + -1x + -2x2 = 0

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

Divide each side by '-2'.
-5.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + 0.5x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + 0.5x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + 0.5x + x2 = 0 + 5.5
0.5x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
0.5x + x2 = 5.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 5.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 5.5 + 0.0625

Combine like terms: 5.5 + 0.0625 = 5.5625
0.0625 + 0.5x + x2 = 5.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(x + 0.25) equal to 2.358495283 and -2.358495283.

Subproblem 1
x + 0.25 = 2.358495283

Simplifying
x + 0.25 = 2.358495283

Reorder the terms:
0.25 + x = 2.358495283

Solving
0.25 + x = 2.358495283

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 2.358495283 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 2.358495283 + -0.25
x = 2.358495283 + -0.25

Combine like terms: 2.358495283 + -0.25 = 2.108495283
x = 2.108495283

Simplifying
x = 2.108495283

Subproblem 2
x + 0.25 = -2.358495283

Simplifying
x + 0.25 = -2.358495283

Reorder the terms:
0.25 + x = -2.358495283

Solving
0.25 + x = -2.358495283

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -2.358495283 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -2.358495283 + -0.25
x = -2.358495283 + -0.25

Combine like terms: -2.358495283 + -0.25 = -2.608495283
x = -2.608495283

Simplifying
x = -2.608495283

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.108495283, -2.608495283}
Solution
x = {2.108495283, -2.608495283}