457x+450=3(6x+50)*450(426884x+1)

Solution for 457x+450=3(6x+50)*450(426884x+1) equation:

Simplifying
457x + 450 = 3(6x + 50) * 450(426884x + 1)

Reorder the terms:
450 + 457x = 3(6x + 50) * 450(426884x + 1)

Reorder the terms:
450 + 457x = 3(50 + 6x) * 450(426884x + 1)

Reorder the terms:
450 + 457x = 3(50 + 6x) * 450(1 + 426884x)

Reorder the terms for easier multiplication:
450 + 457x = 3 * 450(50 + 6x)(1 + 426884x)

Multiply 3 * 450
450 + 457x = 1350(50 + 6x)(1 + 426884x)

Multiply (50 + 6x) * (1 + 426884x)
450 + 457x = 1350(50(1 + 426884x) + 6x * (1 + 426884x))
450 + 457x = 1350((1 * 50 + 426884x * 50) + 6x * (1 + 426884x))
450 + 457x = 1350((50 + 21344200x) + 6x * (1 + 426884x))
450 + 457x = 1350(50 + 21344200x + (1 * 6x + 426884x * 6x))
450 + 457x = 1350(50 + 21344200x + (6x + 2561304x2))

Combine like terms: 21344200x + 6x = 21344206x
450 + 457x = 1350(50 + 21344206x + 2561304x2)
450 + 457x = (50 * 1350 + 21344206x * 1350 + 2561304x2 * 1350)
450 + 457x = (67500 + 28814678100x + 3457760400x2)

Solving
450 + 457x = 67500 + 28814678100x + 3457760400x2

Solving for variable 'x'.

Reorder the terms:
450 + -67500 + 457x + -28814678100x + -3457760400x2 = 67500 + 28814678100x + 3457760400x2 + -67500 + -28814678100x + -3457760400x2

Combine like terms: 450 + -67500 = -67050
-67050 + 457x + -28814678100x + -3457760400x2 = 67500 + 28814678100x + 3457760400x2 + -67500 + -28814678100x + -3457760400x2

Combine like terms: 457x + -28814678100x = -28814677643x
-67050 + -28814677643x + -3457760400x2 = 67500 + 28814678100x + 3457760400x2 + -67500 + -28814678100x + -3457760400x2

Reorder the terms:
-67050 + -28814677643x + -3457760400x2 = 67500 + -67500 + 28814678100x + -28814678100x + 3457760400x2 + -3457760400x2

Combine like terms: 67500 + -67500 = 0
-67050 + -28814677643x + -3457760400x2 = 0 + 28814678100x + -28814678100x + 3457760400x2 + -3457760400x2
-67050 + -28814677643x + -3457760400x2 = 28814678100x + -28814678100x + 3457760400x2 + -3457760400x2

Combine like terms: 28814678100x + -28814678100x = 0
-67050 + -28814677643x + -3457760400x2 = 0 + 3457760400x2 + -3457760400x2
-67050 + -28814677643x + -3457760400x2 = 3457760400x2 + -3457760400x2

Combine like terms: 3457760400x2 + -3457760400x2 = 0
-67050 + -28814677643x + -3457760400x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(67050 + 28814677640x + 3457760400x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(67050 + 28814677640x + 3457760400x2)' equal to zero and attempt to solve:

Simplifying
67050 + 28814677640x + 3457760400x2 = 0

Solving
67050 + 28814677640x + 3457760400x2 = 0

Begin completing the square.  Divide all terms by
3457760400 the coefficient of the squared term: 

Divide each side by '3457760400'.
0.00001939116429 + 8.333335543x + x2 = 0.00

Move the constant term to the right:

Add '-0.00001939116429' to each side of the equation.
0.00001939116429 + 8.333335543x + -0.00001939116429 + x2 = 0.00 + -0.00001939116429

Reorder the terms:
0.00001939116429 + -0.00001939116429 + 8.333335543x + x2 = 0.00 + -0.00001939116429

Combine like terms: 0.00001939116429 + -0.00001939116429 = 0.00000000000000
0.00000000000000 + 8.333335543x + x2 = 0.00 + -0.00001939116429
8.333335543x + x2 = 0.00 + -0.00001939116429

Combine like terms: 0.00 + -0.00001939116429 = -0.00001939116429
8.333335543x + x2 = -0.00001939116429

The x term is 8.333335543x.  Take half its coefficient (4.166667772).
Square it (17.36112032) and add it to both sides.

Add '17.36112032' to each side of the equation.
8.333335543x + 17.36112032 + x2 = -0.00001939116429 + 17.36112032

Reorder the terms:
17.36112032 + 8.333335543x + x2 = -0.00001939116429 + 17.36112032

Combine like terms: -0.00001939116429 + 17.36112032 = 17.36110092883571
17.36112032 + 8.333335543x + x2 = 17.36110092883571

Factor a perfect square on the left side:
(x + 4.166667772)(x + 4.166667772) = 17.36110092883571

Calculate the square root of the right side: 4.166665445

Break this problem into two subproblems by setting 
(x + 4.166667772) equal to 4.166665445 and -4.166665445.

Subproblem 1
x + 4.166667772 = 4.166665445

Simplifying
x + 4.166667772 = 4.166665445

Reorder the terms:
4.166667772 + x = 4.166665445

Solving
4.166667772 + x = 4.166665445

Solving for variable 'x'.

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

Add '-4.166667772' to each side of the equation.
4.166667772 + -4.166667772 + x = 4.166665445 + -4.166667772

Combine like terms: 4.166667772 + -4.166667772 = 0.000000000
0.000000000 + x = 4.166665445 + -4.166667772
x = 4.166665445 + -4.166667772

Combine like terms: 4.166665445 + -4.166667772 = -0.000002327
x = -0.000002327

Simplifying
x = -0.000002327

Subproblem 2
x + 4.166667772 = -4.166665445

Simplifying
x + 4.166667772 = -4.166665445

Reorder the terms:
4.166667772 + x = -4.166665445

Solving
4.166667772 + x = -4.166665445

Solving for variable 'x'.

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

Add '-4.166667772' to each side of the equation.
4.166667772 + -4.166667772 + x = -4.166665445 + -4.166667772

Combine like terms: 4.166667772 + -4.166667772 = 0.000000000
0.000000000 + x = -4.166665445 + -4.166667772
x = -4.166665445 + -4.166667772

Combine like terms: -4.166665445 + -4.166667772 = -8.333333217
x = -8.333333217

Simplifying
x = -8.333333217

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.000002327, -8.333333217}
Solution
x = {-0.000002327, -8.333333217}