(2x-7)(4x-1)-(5x-1)(2x-1)=

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Solution for (2x-7)(4x-1)-(5x-1)(2x-1)= equation:


Simplifying
(2x + -7)(4x + -1) + -1(5x + -1)(2x + -1) = 0

Reorder the terms:
(-7 + 2x)(4x + -1) + -1(5x + -1)(2x + -1) = 0

Reorder the terms:
(-7 + 2x)(-1 + 4x) + -1(5x + -1)(2x + -1) = 0

Multiply (-7 + 2x) * (-1 + 4x)
(-7(-1 + 4x) + 2x * (-1 + 4x)) + -1(5x + -1)(2x + -1) = 0
((-1 * -7 + 4x * -7) + 2x * (-1 + 4x)) + -1(5x + -1)(2x + -1) = 0
((7 + -28x) + 2x * (-1 + 4x)) + -1(5x + -1)(2x + -1) = 0
(7 + -28x + (-1 * 2x + 4x * 2x)) + -1(5x + -1)(2x + -1) = 0
(7 + -28x + (-2x + 8x2)) + -1(5x + -1)(2x + -1) = 0

Combine like terms: -28x + -2x = -30x
(7 + -30x + 8x2) + -1(5x + -1)(2x + -1) = 0

Reorder the terms:
7 + -30x + 8x2 + -1(-1 + 5x)(2x + -1) = 0

Reorder the terms:
7 + -30x + 8x2 + -1(-1 + 5x)(-1 + 2x) = 0

Multiply (-1 + 5x) * (-1 + 2x)
7 + -30x + 8x2 + -1(-1(-1 + 2x) + 5x * (-1 + 2x)) = 0
7 + -30x + 8x2 + -1((-1 * -1 + 2x * -1) + 5x * (-1 + 2x)) = 0
7 + -30x + 8x2 + -1((1 + -2x) + 5x * (-1 + 2x)) = 0
7 + -30x + 8x2 + -1(1 + -2x + (-1 * 5x + 2x * 5x)) = 0
7 + -30x + 8x2 + -1(1 + -2x + (-5x + 10x2)) = 0

Combine like terms: -2x + -5x = -7x
7 + -30x + 8x2 + -1(1 + -7x + 10x2) = 0
7 + -30x + 8x2 + (1 * -1 + -7x * -1 + 10x2 * -1) = 0
7 + -30x + 8x2 + (-1 + 7x + -10x2) = 0

Reorder the terms:
7 + -1 + -30x + 7x + 8x2 + -10x2 = 0

Combine like terms: 7 + -1 = 6
6 + -30x + 7x + 8x2 + -10x2 = 0

Combine like terms: -30x + 7x = -23x
6 + -23x + 8x2 + -10x2 = 0

Combine like terms: 8x2 + -10x2 = -2x2
6 + -23x + -2x2 = 0

Solving
6 + -23x + -2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-3 + 11.5x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 11.5x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 11.5x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 11.5x + x2 = 0 + 3
11.5x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
11.5x + x2 = 3

The x term is 11.5x.  Take half its coefficient (5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
11.5x + 33.0625 + x2 = 3 + 33.0625

Reorder the terms:
33.0625 + 11.5x + x2 = 3 + 33.0625

Combine like terms: 3 + 33.0625 = 36.0625
33.0625 + 11.5x + x2 = 36.0625

Factor a perfect square on the left side:
(x + 5.75)(x + 5.75) = 36.0625

Calculate the square root of the right side: 6.005206075

Break this problem into two subproblems by setting 
(x + 5.75) equal to 6.005206075 and -6.005206075.

Subproblem 1

x + 5.75 = 6.005206075 Simplifying x + 5.75 = 6.005206075 Reorder the terms: 5.75 + x = 6.005206075 Solving 5.75 + x = 6.005206075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = 6.005206075 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = 6.005206075 + -5.75 x = 6.005206075 + -5.75 Combine like terms: 6.005206075 + -5.75 = 0.255206075 x = 0.255206075 Simplifying x = 0.255206075

Subproblem 2

x + 5.75 = -6.005206075 Simplifying x + 5.75 = -6.005206075 Reorder the terms: 5.75 + x = -6.005206075 Solving 5.75 + x = -6.005206075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = -6.005206075 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = -6.005206075 + -5.75 x = -6.005206075 + -5.75 Combine like terms: -6.005206075 + -5.75 = -11.755206075 x = -11.755206075 Simplifying x = -11.755206075

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.255206075, -11.755206075}

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