(3x-5)(2x-25)=(25x-8)

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Solution for (3x-5)(2x-25)=(25x-8) equation:


Simplifying
(3x + -5)(2x + -25) = (25x + -8)

Reorder the terms:
(-5 + 3x)(2x + -25) = (25x + -8)

Reorder the terms:
(-5 + 3x)(-25 + 2x) = (25x + -8)

Multiply (-5 + 3x) * (-25 + 2x)
(-5(-25 + 2x) + 3x * (-25 + 2x)) = (25x + -8)
((-25 * -5 + 2x * -5) + 3x * (-25 + 2x)) = (25x + -8)
((125 + -10x) + 3x * (-25 + 2x)) = (25x + -8)
(125 + -10x + (-25 * 3x + 2x * 3x)) = (25x + -8)
(125 + -10x + (-75x + 6x2)) = (25x + -8)

Combine like terms: -10x + -75x = -85x
(125 + -85x + 6x2) = (25x + -8)

Reorder the terms:
125 + -85x + 6x2 = (-8 + 25x)

Remove parenthesis around (-8 + 25x)
125 + -85x + 6x2 = -8 + 25x

Solving
125 + -85x + 6x2 = -8 + 25x

Solving for variable 'x'.

Reorder the terms:
125 + 8 + -85x + -25x + 6x2 = -8 + 25x + 8 + -25x

Combine like terms: 125 + 8 = 133
133 + -85x + -25x + 6x2 = -8 + 25x + 8 + -25x

Combine like terms: -85x + -25x = -110x
133 + -110x + 6x2 = -8 + 25x + 8 + -25x

Reorder the terms:
133 + -110x + 6x2 = -8 + 8 + 25x + -25x

Combine like terms: -8 + 8 = 0
133 + -110x + 6x2 = 0 + 25x + -25x
133 + -110x + 6x2 = 25x + -25x

Combine like terms: 25x + -25x = 0
133 + -110x + 6x2 = 0

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

Divide each side by '6'.
22.16666667 + -18.33333333x + x2 = 0

Move the constant term to the right:

Add '-22.16666667' to each side of the equation.
22.16666667 + -18.33333333x + -22.16666667 + x2 = 0 + -22.16666667

Reorder the terms:
22.16666667 + -22.16666667 + -18.33333333x + x2 = 0 + -22.16666667

Combine like terms: 22.16666667 + -22.16666667 = 0.00000000
0.00000000 + -18.33333333x + x2 = 0 + -22.16666667
-18.33333333x + x2 = 0 + -22.16666667

Combine like terms: 0 + -22.16666667 = -22.16666667
-18.33333333x + x2 = -22.16666667

The x term is -18.33333333x.  Take half its coefficient (-9.166666665).
Square it (84.02777775) and add it to both sides.

Add '84.02777775' to each side of the equation.
-18.33333333x + 84.02777775 + x2 = -22.16666667 + 84.02777775

Reorder the terms:
84.02777775 + -18.33333333x + x2 = -22.16666667 + 84.02777775

Combine like terms: -22.16666667 + 84.02777775 = 61.86111108
84.02777775 + -18.33333333x + x2 = 61.86111108

Factor a perfect square on the left side:
(x + -9.166666665)(x + -9.166666665) = 61.86111108

Calculate the square root of the right side: 7.865183474

Break this problem into two subproblems by setting 
(x + -9.166666665) equal to 7.865183474 and -7.865183474.


Subproblem 1
x + -9.166666665 = 7.865183474

Simplifying
x + -9.166666665 = 7.865183474

Reorder the terms:
-9.166666665 + x = 7.865183474

Solving
-9.166666665 + x = 7.865183474

Solving for variable 'x'.

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

Add '9.166666665' to each side of the equation.
-9.166666665 + 9.166666665 + x = 7.865183474 + 9.166666665

Combine like terms: -9.166666665 + 9.166666665 = 0.000000000
0.000000000 + x = 7.865183474 + 9.166666665
x = 7.865183474 + 9.166666665

Combine like terms: 7.865183474 + 9.166666665 = 17.031850139
x = 17.031850139

Simplifying
x = 17.031850139


Subproblem 2
x + -9.166666665 = -7.865183474

Simplifying
x + -9.166666665 = -7.865183474

Reorder the terms:
-9.166666665 + x = -7.865183474

Solving
-9.166666665 + x = -7.865183474

Solving for variable 'x'.

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

Add '9.166666665' to each side of the equation.
-9.166666665 + 9.166666665 + x = -7.865183474 + 9.166666665

Combine like terms: -9.166666665 + 9.166666665 = 0.000000000
0.000000000 + x = -7.865183474 + 9.166666665
x = -7.865183474 + 9.166666665

Combine like terms: -7.865183474 + 9.166666665 = 1.301483191
x = 1.301483191

Simplifying
x = 1.301483191


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.031850139, 1.301483191}

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