(23x-2)*(2x-2-90-80x)=90-907

Solution for (23x-2)*(2x-2-90-80x)=90-907 equation:

Simplifying
(23x + -2)(2x + -2 + -90 + -80x) = 90 + -907

Reorder the terms:
(-2 + 23x)(2x + -2 + -90 + -80x) = 90 + -907

Reorder the terms:
(-2 + 23x)(-2 + -90 + 2x + -80x) = 90 + -907

Combine like terms: -2 + -90 = -92
(-2 + 23x)(-92 + 2x + -80x) = 90 + -907

Combine like terms: 2x + -80x = -78x
(-2 + 23x)(-92 + -78x) = 90 + -907

Multiply (-2 + 23x) * (-92 + -78x)
(-2(-92 + -78x) + 23x * (-92 + -78x)) = 90 + -907
((-92 * -2 + -78x * -2) + 23x * (-92 + -78x)) = 90 + -907
((184 + 156x) + 23x * (-92 + -78x)) = 90 + -907
(184 + 156x + (-92 * 23x + -78x * 23x)) = 90 + -907
(184 + 156x + (-2116x + -1794x2)) = 90 + -907

Combine like terms: 156x + -2116x = -1960x
(184 + -1960x + -1794x2) = 90 + -907

Combine like terms: 90 + -907 = -817
184 + -1960x + -1794x2 = -817

Solving
184 + -1960x + -1794x2 = -817

Solving for variable 'x'.

Reorder the terms:
184 + 817 + -1960x + -1794x2 = -817 + 817

Combine like terms: 184 + 817 = 1001
1001 + -1960x + -1794x2 = -817 + 817

Combine like terms: -817 + 817 = 0
1001 + -1960x + -1794x2 = 0

Begin completing the square.  Divide all terms by
-1794 the coefficient of the squared term: 

Divide each side by '-1794'.
-0.5579710145 + 1.092530658x + x2 = 0

Move the constant term to the right:

Add '0.5579710145' to each side of the equation.
-0.5579710145 + 1.092530658x + 0.5579710145 + x2 = 0 + 0.5579710145

Reorder the terms:
-0.5579710145 + 0.5579710145 + 1.092530658x + x2 = 0 + 0.5579710145

Combine like terms: -0.5579710145 + 0.5579710145 = 0.0000000000
0.0000000000 + 1.092530658x + x2 = 0 + 0.5579710145
1.092530658x + x2 = 0 + 0.5579710145

Combine like terms: 0 + 0.5579710145 = 0.5579710145
1.092530658x + x2 = 0.5579710145

The x term is 1.092530658x.  Take half its coefficient (0.546265329).
Square it (0.2984058097) and add it to both sides.

Add '0.2984058097' to each side of the equation.
1.092530658x + 0.2984058097 + x2 = 0.5579710145 + 0.2984058097

Reorder the terms:
0.2984058097 + 1.092530658x + x2 = 0.5579710145 + 0.2984058097

Combine like terms: 0.5579710145 + 0.2984058097 = 0.8563768242
0.2984058097 + 1.092530658x + x2 = 0.8563768242

Factor a perfect square on the left side:
(x + 0.546265329)(x + 0.546265329) = 0.8563768242

Calculate the square root of the right side: 0.925406302

Break this problem into two subproblems by setting 
(x + 0.546265329) equal to 0.925406302 and -0.925406302.

Subproblem 1
x + 0.546265329 = 0.925406302

Simplifying
x + 0.546265329 = 0.925406302

Reorder the terms:
0.546265329 + x = 0.925406302

Solving
0.546265329 + x = 0.925406302

Solving for variable 'x'.

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

Add '-0.546265329' to each side of the equation.
0.546265329 + -0.546265329 + x = 0.925406302 + -0.546265329

Combine like terms: 0.546265329 + -0.546265329 = 0.000000000
0.000000000 + x = 0.925406302 + -0.546265329
x = 0.925406302 + -0.546265329

Combine like terms: 0.925406302 + -0.546265329 = 0.379140973
x = 0.379140973

Simplifying
x = 0.379140973

Subproblem 2
x + 0.546265329 = -0.925406302

Simplifying
x + 0.546265329 = -0.925406302

Reorder the terms:
0.546265329 + x = -0.925406302

Solving
0.546265329 + x = -0.925406302

Solving for variable 'x'.

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

Add '-0.546265329' to each side of the equation.
0.546265329 + -0.546265329 + x = -0.925406302 + -0.546265329

Combine like terms: 0.546265329 + -0.546265329 = 0.000000000
0.000000000 + x = -0.925406302 + -0.546265329
x = -0.925406302 + -0.546265329

Combine like terms: -0.925406302 + -0.546265329 = -1.471671631
x = -1.471671631

Simplifying
x = -1.471671631

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.379140973, -1.471671631}