-8x(22x+23)+17x-28x=-25-(18x+21)

Solution for -8x(22x+23)+17x-28x=-25-(18x+21) equation:

Simplifying
-8x(22x + 23) + 17x + -28x = -25 + -1(18x + 21)

Reorder the terms:
-8x(23 + 22x) + 17x + -28x = -25 + -1(18x + 21)
(23 * -8x + 22x * -8x) + 17x + -28x = -25 + -1(18x + 21)
(-184x + -176x2) + 17x + -28x = -25 + -1(18x + 21)

Reorder the terms:
-184x + 17x + -28x + -176x2 = -25 + -1(18x + 21)

Combine like terms: -184x + 17x = -167x
-167x + -28x + -176x2 = -25 + -1(18x + 21)

Combine like terms: -167x + -28x = -195x
-195x + -176x2 = -25 + -1(18x + 21)

Reorder the terms:
-195x + -176x2 = -25 + -1(21 + 18x)
-195x + -176x2 = -25 + (21 * -1 + 18x * -1)
-195x + -176x2 = -25 + (-21 + -18x)

Combine like terms: -25 + -21 = -46
-195x + -176x2 = -46 + -18x

Solving
-195x + -176x2 = -46 + -18x

Solving for variable 'x'.

Reorder the terms:
46 + -195x + 18x + -176x2 = -46 + -18x + 46 + 18x

Combine like terms: -195x + 18x = -177x
46 + -177x + -176x2 = -46 + -18x + 46 + 18x

Reorder the terms:
46 + -177x + -176x2 = -46 + 46 + -18x + 18x

Combine like terms: -46 + 46 = 0
46 + -177x + -176x2 = 0 + -18x + 18x
46 + -177x + -176x2 = -18x + 18x

Combine like terms: -18x + 18x = 0
46 + -177x + -176x2 = 0

Begin completing the square.  Divide all terms by
-176 the coefficient of the squared term: 

Divide each side by '-176'.
-0.2613636364 + 1.005681818x + x2 = 0

Move the constant term to the right:

Add '0.2613636364' to each side of the equation.
-0.2613636364 + 1.005681818x + 0.2613636364 + x2 = 0 + 0.2613636364

Reorder the terms:
-0.2613636364 + 0.2613636364 + 1.005681818x + x2 = 0 + 0.2613636364

Combine like terms: -0.2613636364 + 0.2613636364 = 0.0000000000
0.0000000000 + 1.005681818x + x2 = 0 + 0.2613636364
1.005681818x + x2 = 0 + 0.2613636364

Combine like terms: 0 + 0.2613636364 = 0.2613636364
1.005681818x + x2 = 0.2613636364

The x term is 1.005681818x.  Take half its coefficient (0.502840909).
Square it (0.2528489798) and add it to both sides.

Add '0.2528489798' to each side of the equation.
1.005681818x + 0.2528489798 + x2 = 0.2613636364 + 0.2528489798

Reorder the terms:
0.2528489798 + 1.005681818x + x2 = 0.2613636364 + 0.2528489798

Combine like terms: 0.2613636364 + 0.2528489798 = 0.5142126162
0.2528489798 + 1.005681818x + x2 = 0.5142126162

Factor a perfect square on the left side:
(x + 0.502840909)(x + 0.502840909) = 0.5142126162

Calculate the square root of the right side: 0.717086199

Break this problem into two subproblems by setting 
(x + 0.502840909) equal to 0.717086199 and -0.717086199.

Subproblem 1
x + 0.502840909 = 0.717086199

Simplifying
x + 0.502840909 = 0.717086199

Reorder the terms:
0.502840909 + x = 0.717086199

Solving
0.502840909 + x = 0.717086199

Solving for variable 'x'.

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

Add '-0.502840909' to each side of the equation.
0.502840909 + -0.502840909 + x = 0.717086199 + -0.502840909

Combine like terms: 0.502840909 + -0.502840909 = 0.000000000
0.000000000 + x = 0.717086199 + -0.502840909
x = 0.717086199 + -0.502840909

Combine like terms: 0.717086199 + -0.502840909 = 0.21424529
x = 0.21424529

Simplifying
x = 0.21424529

Subproblem 2
x + 0.502840909 = -0.717086199

Simplifying
x + 0.502840909 = -0.717086199

Reorder the terms:
0.502840909 + x = -0.717086199

Solving
0.502840909 + x = -0.717086199

Solving for variable 'x'.

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

Add '-0.502840909' to each side of the equation.
0.502840909 + -0.502840909 + x = -0.717086199 + -0.502840909

Combine like terms: 0.502840909 + -0.502840909 = 0.000000000
0.000000000 + x = -0.717086199 + -0.502840909
x = -0.717086199 + -0.502840909

Combine like terms: -0.717086199 + -0.502840909 = -1.219927108
x = -1.219927108

Simplifying
x = -1.219927108

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.21424529, -1.219927108}