(5x-4)-(3x+5)(2x-1)=20x(x-2)+27

Solution for (5x-4)-(3x+5)(2x-1)=20x(x-2)+27 equation:

Simplifying
(5x + -4) + -1(3x + 5)(2x + -1) = 20x(x + -2) + 27

Reorder the terms:
(-4 + 5x) + -1(3x + 5)(2x + -1) = 20x(x + -2) + 27

Remove parenthesis around (-4 + 5x)
-4 + 5x + -1(3x + 5)(2x + -1) = 20x(x + -2) + 27

Reorder the terms:
-4 + 5x + -1(5 + 3x)(2x + -1) = 20x(x + -2) + 27

Reorder the terms:
-4 + 5x + -1(5 + 3x)(-1 + 2x) = 20x(x + -2) + 27

Multiply (5 + 3x) * (-1 + 2x)
-4 + 5x + -1(5(-1 + 2x) + 3x * (-1 + 2x)) = 20x(x + -2) + 27
-4 + 5x + -1((-1 * 5 + 2x * 5) + 3x * (-1 + 2x)) = 20x(x + -2) + 27
-4 + 5x + -1((-5 + 10x) + 3x * (-1 + 2x)) = 20x(x + -2) + 27
-4 + 5x + -1(-5 + 10x + (-1 * 3x + 2x * 3x)) = 20x(x + -2) + 27
-4 + 5x + -1(-5 + 10x + (-3x + 6x2)) = 20x(x + -2) + 27

Combine like terms: 10x + -3x = 7x
-4 + 5x + -1(-5 + 7x + 6x2) = 20x(x + -2) + 27
-4 + 5x + (-5 * -1 + 7x * -1 + 6x2 * -1) = 20x(x + -2) + 27
-4 + 5x + (5 + -7x + -6x2) = 20x(x + -2) + 27

Reorder the terms:
-4 + 5 + 5x + -7x + -6x2 = 20x(x + -2) + 27

Combine like terms: -4 + 5 = 1
1 + 5x + -7x + -6x2 = 20x(x + -2) + 27

Combine like terms: 5x + -7x = -2x
1 + -2x + -6x2 = 20x(x + -2) + 27

Reorder the terms:
1 + -2x + -6x2 = 20x(-2 + x) + 27
1 + -2x + -6x2 = (-2 * 20x + x * 20x) + 27
1 + -2x + -6x2 = (-40x + 20x2) + 27

Reorder the terms:
1 + -2x + -6x2 = 27 + -40x + 20x2

Solving
1 + -2x + -6x2 = 27 + -40x + 20x2

Solving for variable 'x'.

Reorder the terms:
1 + -27 + -2x + 40x + -6x2 + -20x2 = 27 + -40x + 20x2 + -27 + 40x + -20x2

Combine like terms: 1 + -27 = -26
-26 + -2x + 40x + -6x2 + -20x2 = 27 + -40x + 20x2 + -27 + 40x + -20x2

Combine like terms: -2x + 40x = 38x
-26 + 38x + -6x2 + -20x2 = 27 + -40x + 20x2 + -27 + 40x + -20x2

Combine like terms: -6x2 + -20x2 = -26x2
-26 + 38x + -26x2 = 27 + -40x + 20x2 + -27 + 40x + -20x2

Reorder the terms:
-26 + 38x + -26x2 = 27 + -27 + -40x + 40x + 20x2 + -20x2

Combine like terms: 27 + -27 = 0
-26 + 38x + -26x2 = 0 + -40x + 40x + 20x2 + -20x2
-26 + 38x + -26x2 = -40x + 40x + 20x2 + -20x2

Combine like terms: -40x + 40x = 0
-26 + 38x + -26x2 = 0 + 20x2 + -20x2
-26 + 38x + -26x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
-26 + 38x + -26x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 19x + -13x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-13 + 19x + -13x2)' equal to zero and attempt to solve:

Simplifying
-13 + 19x + -13x2 = 0

Solving
-13 + 19x + -13x2 = 0

Begin completing the square.  Divide all terms by
-13 the coefficient of the squared term: 

Divide each side by '-13'.
1 + -1.461538462x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1.461538462x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -1.461538462x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1.461538462x + x2 = 0 + -1
-1.461538462x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1.461538462x + x2 = -1

The x term is -1.461538462x.  Take half its coefficient (-0.730769231).
Square it (0.5340236690) and add it to both sides.

Add '0.5340236690' to each side of the equation.
-1.461538462x + 0.5340236690 + x2 = -1 + 0.5340236690

Reorder the terms:
0.5340236690 + -1.461538462x + x2 = -1 + 0.5340236690

Combine like terms: -1 + 0.5340236690 = -0.465976331
0.5340236690 + -1.461538462x + x2 = -0.465976331

Factor a perfect square on the left side:
(x + -0.730769231)(x + -0.730769231) = -0.465976331

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.