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

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


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

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

Reorder the terms for easier multiplication:
2(-4 + 5x) + -1(3x + 5)(2x + -1) = 20x(x + -2) + 27
(-4 * 2 + 5x * 2) + -1(3x + 5)(2x + -1) = 20x(x + -2) + 27
(-8 + 10x) + -1(3x + 5)(2x + -1) = 20x(x + -2) + 27

Reorder the terms:
-8 + 10x + -1(5 + 3x)(2x + -1) = 20x(x + -2) + 27

Reorder the terms:
-8 + 10x + -1(5 + 3x)(-1 + 2x) = 20x(x + -2) + 27

Multiply (5 + 3x) * (-1 + 2x)
-8 + 10x + -1(5(-1 + 2x) + 3x * (-1 + 2x)) = 20x(x + -2) + 27
-8 + 10x + -1((-1 * 5 + 2x * 5) + 3x * (-1 + 2x)) = 20x(x + -2) + 27
-8 + 10x + -1((-5 + 10x) + 3x * (-1 + 2x)) = 20x(x + -2) + 27
-8 + 10x + -1(-5 + 10x + (-1 * 3x + 2x * 3x)) = 20x(x + -2) + 27
-8 + 10x + -1(-5 + 10x + (-3x + 6x2)) = 20x(x + -2) + 27

Combine like terms: 10x + -3x = 7x
-8 + 10x + -1(-5 + 7x + 6x2) = 20x(x + -2) + 27
-8 + 10x + (-5 * -1 + 7x * -1 + 6x2 * -1) = 20x(x + -2) + 27
-8 + 10x + (5 + -7x + -6x2) = 20x(x + -2) + 27

Reorder the terms:
-8 + 5 + 10x + -7x + -6x2 = 20x(x + -2) + 27

Combine like terms: -8 + 5 = -3
-3 + 10x + -7x + -6x2 = 20x(x + -2) + 27

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

Reorder the terms:
-3 + 3x + -6x2 = 20x(-2 + x) + 27
-3 + 3x + -6x2 = (-2 * 20x + x * 20x) + 27
-3 + 3x + -6x2 = (-40x + 20x2) + 27

Reorder the terms:
-3 + 3x + -6x2 = 27 + -40x + 20x2

Solving
-3 + 3x + -6x2 = 27 + -40x + 20x2

Solving for variable 'x'.

Reorder the terms:
-3 + -27 + 3x + 40x + -6x2 + -20x2 = 27 + -40x + 20x2 + -27 + 40x + -20x2

Combine like terms: -3 + -27 = -30
-30 + 3x + 40x + -6x2 + -20x2 = 27 + -40x + 20x2 + -27 + 40x + -20x2

Combine like terms: 3x + 40x = 43x
-30 + 43x + -6x2 + -20x2 = 27 + -40x + 20x2 + -27 + 40x + -20x2

Combine like terms: -6x2 + -20x2 = -26x2
-30 + 43x + -26x2 = 27 + -40x + 20x2 + -27 + 40x + -20x2

Reorder the terms:
-30 + 43x + -26x2 = 27 + -27 + -40x + 40x + 20x2 + -20x2

Combine like terms: 27 + -27 = 0
-30 + 43x + -26x2 = 0 + -40x + 40x + 20x2 + -20x2
-30 + 43x + -26x2 = -40x + 40x + 20x2 + -20x2

Combine like terms: -40x + 40x = 0
-30 + 43x + -26x2 = 0 + 20x2 + -20x2
-30 + 43x + -26x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
-30 + 43x + -26x2 = 0

Begin completing the square.  Divide all terms by
-26 the coefficient of the squared term: 

Divide each side by '-26'.
1.153846154 + -1.653846154x + x2 = 0

Move the constant term to the right:

Add '-1.153846154' to each side of the equation.
1.153846154 + -1.653846154x + -1.153846154 + x2 = 0 + -1.153846154

Reorder the terms:
1.153846154 + -1.153846154 + -1.653846154x + x2 = 0 + -1.153846154

Combine like terms: 1.153846154 + -1.153846154 = 0.000000000
0.000000000 + -1.653846154x + x2 = 0 + -1.153846154
-1.653846154x + x2 = 0 + -1.153846154

Combine like terms: 0 + -1.153846154 = -1.153846154
-1.653846154x + x2 = -1.153846154

The x term is -1.653846154x.  Take half its coefficient (-0.826923077).
Square it (0.6838017753) and add it to both sides.

Add '0.6838017753' to each side of the equation.
-1.653846154x + 0.6838017753 + x2 = -1.153846154 + 0.6838017753

Reorder the terms:
0.6838017753 + -1.653846154x + x2 = -1.153846154 + 0.6838017753

Combine like terms: -1.153846154 + 0.6838017753 = -0.4700443787
0.6838017753 + -1.653846154x + x2 = -0.4700443787

Factor a perfect square on the left side:
(x + -0.826923077)(x + -0.826923077) = -0.4700443787

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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