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

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

Simplifying
x = (5x + -4)(7x + -5)

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

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

Multiply (-4 + 5x) * (-5 + 7x)
x = (-4(-5 + 7x) + 5x * (-5 + 7x))
x = ((-5 * -4 + 7x * -4) + 5x * (-5 + 7x))
x = ((20 + -28x) + 5x * (-5 + 7x))
x = (20 + -28x + (-5 * 5x + 7x * 5x))
x = (20 + -28x + (-25x + 35x2))

Combine like terms: -28x + -25x = -53x
x = (20 + -53x + 35x2)

Solving
x = 20 + -53x + 35x2

Solving for variable 'x'.

Reorder the terms:
-20 + x + 53x + -35x2 = 20 + -53x + 35x2 + -20 + 53x + -35x2

Combine like terms: x + 53x = 54x
-20 + 54x + -35x2 = 20 + -53x + 35x2 + -20 + 53x + -35x2

Reorder the terms:
-20 + 54x + -35x2 = 20 + -20 + -53x + 53x + 35x2 + -35x2

Combine like terms: 20 + -20 = 0
-20 + 54x + -35x2 = 0 + -53x + 53x + 35x2 + -35x2
-20 + 54x + -35x2 = -53x + 53x + 35x2 + -35x2

Combine like terms: -53x + 53x = 0
-20 + 54x + -35x2 = 0 + 35x2 + -35x2
-20 + 54x + -35x2 = 35x2 + -35x2

Combine like terms: 35x2 + -35x2 = 0
-20 + 54x + -35x2 = 0

Begin completing the square.  Divide all terms by
-35 the coefficient of the squared term: 

Divide each side by '-35'.
0.5714285714 + -1.542857143x + x2 = 0

Move the constant term to the right:

Add '-0.5714285714' to each side of the equation.
0.5714285714 + -1.542857143x + -0.5714285714 + x2 = 0 + -0.5714285714

Reorder the terms:
0.5714285714 + -0.5714285714 + -1.542857143x + x2 = 0 + -0.5714285714

Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000
0.0000000000 + -1.542857143x + x2 = 0 + -0.5714285714
-1.542857143x + x2 = 0 + -0.5714285714

Combine like terms: 0 + -0.5714285714 = -0.5714285714
-1.542857143x + x2 = -0.5714285714

The x term is -1.542857143x.  Take half its coefficient (-0.7714285715).
Square it (0.5951020409) and add it to both sides.

Add '0.5951020409' to each side of the equation.
-1.542857143x + 0.5951020409 + x2 = -0.5714285714 + 0.5951020409

Reorder the terms:
0.5951020409 + -1.542857143x + x2 = -0.5714285714 + 0.5951020409

Combine like terms: -0.5714285714 + 0.5951020409 = 0.0236734695
0.5951020409 + -1.542857143x + x2 = 0.0236734695

Factor a perfect square on the left side:
(x + -0.7714285715)(x + -0.7714285715) = 0.0236734695

Calculate the square root of the right side: 0.153861852

Break this problem into two subproblems by setting 
(x + -0.7714285715) equal to 0.153861852 and -0.153861852.

Subproblem 1
x + -0.7714285715 = 0.153861852

Simplifying
x + -0.7714285715 = 0.153861852

Reorder the terms:
-0.7714285715 + x = 0.153861852

Solving
-0.7714285715 + x = 0.153861852

Solving for variable 'x'.

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

Add '0.7714285715' to each side of the equation.
-0.7714285715 + 0.7714285715 + x = 0.153861852 + 0.7714285715

Combine like terms: -0.7714285715 + 0.7714285715 = 0.0000000000
0.0000000000 + x = 0.153861852 + 0.7714285715
x = 0.153861852 + 0.7714285715

Combine like terms: 0.153861852 + 0.7714285715 = 0.9252904235
x = 0.9252904235

Simplifying
x = 0.9252904235

Subproblem 2
x + -0.7714285715 = -0.153861852

Simplifying
x + -0.7714285715 = -0.153861852

Reorder the terms:
-0.7714285715 + x = -0.153861852

Solving
-0.7714285715 + x = -0.153861852

Solving for variable 'x'.

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

Add '0.7714285715' to each side of the equation.
-0.7714285715 + 0.7714285715 + x = -0.153861852 + 0.7714285715

Combine like terms: -0.7714285715 + 0.7714285715 = 0.0000000000
0.0000000000 + x = -0.153861852 + 0.7714285715
x = -0.153861852 + 0.7714285715

Combine like terms: -0.153861852 + 0.7714285715 = 0.6175667195
x = 0.6175667195

Simplifying
x = 0.6175667195

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9252904235, 0.6175667195}