(2x-1)(4x-1)-(4x-5)(6x-1)=

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Solution for (2x-1)(4x-1)-(4x-5)(6x-1)= equation: 


Simplifying
(2x + -1)(4x + -1) + -1(4x + -5)(6x + -1) = 0

Reorder the terms:
(-1 + 2x)(4x + -1) + -1(4x + -5)(6x + -1) = 0

Reorder the terms:
(-1 + 2x)(-1 + 4x) + -1(4x + -5)(6x + -1) = 0

Multiply (-1 + 2x) * (-1 + 4x)
(-1(-1 + 4x) + 2x * (-1 + 4x)) + -1(4x + -5)(6x + -1) = 0
((-1 * -1 + 4x * -1) + 2x * (-1 + 4x)) + -1(4x + -5)(6x + -1) = 0
((1 + -4x) + 2x * (-1 + 4x)) + -1(4x + -5)(6x + -1) = 0
(1 + -4x + (-1 * 2x + 4x * 2x)) + -1(4x + -5)(6x + -1) = 0
(1 + -4x + (-2x + 8x2)) + -1(4x + -5)(6x + -1) = 0

Combine like terms: -4x + -2x = -6x
(1 + -6x + 8x2) + -1(4x + -5)(6x + -1) = 0

Reorder the terms:
1 + -6x + 8x2 + -1(-5 + 4x)(6x + -1) = 0

Reorder the terms:
1 + -6x + 8x2 + -1(-5 + 4x)(-1 + 6x) = 0

Multiply (-5 + 4x) * (-1 + 6x)
1 + -6x + 8x2 + -1(-5(-1 + 6x) + 4x * (-1 + 6x)) = 0
1 + -6x + 8x2 + -1((-1 * -5 + 6x * -5) + 4x * (-1 + 6x)) = 0
1 + -6x + 8x2 + -1((5 + -30x) + 4x * (-1 + 6x)) = 0
1 + -6x + 8x2 + -1(5 + -30x + (-1 * 4x + 6x * 4x)) = 0
1 + -6x + 8x2 + -1(5 + -30x + (-4x + 24x2)) = 0

Combine like terms: -30x + -4x = -34x
1 + -6x + 8x2 + -1(5 + -34x + 24x2) = 0
1 + -6x + 8x2 + (5 * -1 + -34x * -1 + 24x2 * -1) = 0
1 + -6x + 8x2 + (-5 + 34x + -24x2) = 0

Reorder the terms:
1 + -5 + -6x + 34x + 8x2 + -24x2 = 0

Combine like terms: 1 + -5 = -4
-4 + -6x + 34x + 8x2 + -24x2 = 0

Combine like terms: -6x + 34x = 28x
-4 + 28x + 8x2 + -24x2 = 0

Combine like terms: 8x2 + -24x2 = -16x2
-4 + 28x + -16x2 = 0

Solving
-4 + 28x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 7x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + 7x + -4x2)' equal to zero and attempt to solve:

Simplifying
-1 + 7x + -4x2 = 0

Solving
-1 + 7x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.25 + -1.75x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1.75x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1.75x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1.75x + x2 = 0 + -0.25
-1.75x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1.75x + x2 = -0.25

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = -0.25 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = -0.25 + 0.765625

Combine like terms: -0.25 + 0.765625 = 0.515625
0.765625 + -1.75x + x2 = 0.515625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(x + -0.875) equal to 0.718070331 and -0.718070331.


Subproblem 1
x + -0.875 = 0.718070331

Simplifying
x + -0.875 = 0.718070331

Reorder the terms:
-0.875 + x = 0.718070331

Solving
-0.875 + x = 0.718070331

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 0.718070331 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 0.718070331 + 0.875
x = 0.718070331 + 0.875

Combine like terms: 0.718070331 + 0.875 = 1.593070331
x = 1.593070331

Simplifying
x = 1.593070331


Subproblem 2
x + -0.875 = -0.718070331

Simplifying
x + -0.875 = -0.718070331

Reorder the terms:
-0.875 + x = -0.718070331

Solving
-0.875 + x = -0.718070331

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -0.718070331 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -0.718070331 + 0.875
x = -0.718070331 + 0.875

Combine like terms: -0.718070331 + 0.875 = 0.156929669
x = 0.156929669

Simplifying
x = 0.156929669


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.593070331, 0.156929669}
Solution
x = {1.593070331, 0.156929669}

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