0=((7x-3)(5x-7))-((2x-3)(5x-2))

Solution for 0=((7x-3)(5x-7))-((2x-3)(5x-2)) equation:

Simplifying
0 = ((7x + -3)(5x + -7)) + -1((2x + -3)(5x + -2))

Reorder the terms:
0 = ((-3 + 7x)(5x + -7)) + -1((2x + -3)(5x + -2))

Reorder the terms:
0 = ((-3 + 7x)(-7 + 5x)) + -1((2x + -3)(5x + -2))

Multiply (-3 + 7x) * (-7 + 5x)
0 = ((-3(-7 + 5x) + 7x * (-7 + 5x))) + -1((2x + -3)(5x + -2))
0 = (((-7 * -3 + 5x * -3) + 7x * (-7 + 5x))) + -1((2x + -3)(5x + -2))
0 = (((21 + -15x) + 7x * (-7 + 5x))) + -1((2x + -3)(5x + -2))
0 = ((21 + -15x + (-7 * 7x + 5x * 7x))) + -1((2x + -3)(5x + -2))
0 = ((21 + -15x + (-49x + 35x2))) + -1((2x + -3)(5x + -2))

Combine like terms: -15x + -49x = -64x
0 = ((21 + -64x + 35x2)) + -1((2x + -3)(5x + -2))
0 = (21 + -64x + 35x2) + -1((2x + -3)(5x + -2))

Remove parenthesis around (21 + -64x + 35x2)
0 = 21 + -64x + 35x2 + -1((2x + -3)(5x + -2))

Reorder the terms:
0 = 21 + -64x + 35x2 + -1((-3 + 2x)(5x + -2))

Reorder the terms:
0 = 21 + -64x + 35x2 + -1((-3 + 2x)(-2 + 5x))

Multiply (-3 + 2x) * (-2 + 5x)
0 = 21 + -64x + 35x2 + -1((-3(-2 + 5x) + 2x * (-2 + 5x)))
0 = 21 + -64x + 35x2 + -1(((-2 * -3 + 5x * -3) + 2x * (-2 + 5x)))
0 = 21 + -64x + 35x2 + -1(((6 + -15x) + 2x * (-2 + 5x)))
0 = 21 + -64x + 35x2 + -1((6 + -15x + (-2 * 2x + 5x * 2x)))
0 = 21 + -64x + 35x2 + -1((6 + -15x + (-4x + 10x2)))

Combine like terms: -15x + -4x = -19x
0 = 21 + -64x + 35x2 + -1((6 + -19x + 10x2))
0 = 21 + -64x + 35x2 + (6 * -1 + -19x * -1 + 10x2 * -1)
0 = 21 + -64x + 35x2 + (-6 + 19x + -10x2)

Reorder the terms:
0 = 21 + -6 + -64x + 19x + 35x2 + -10x2

Combine like terms: 21 + -6 = 15
0 = 15 + -64x + 19x + 35x2 + -10x2

Combine like terms: -64x + 19x = -45x
0 = 15 + -45x + 35x2 + -10x2

Combine like terms: 35x2 + -10x2 = 25x2
0 = 15 + -45x + 25x2

Solving
0 = 15 + -45x + 25x2

Solving for variable 'x'.

Combine like terms: 0 + -15 = -15
-15 + 45x + -25x2 = 15 + -45x + 25x2 + -15 + 45x + -25x2

Reorder the terms:
-15 + 45x + -25x2 = 15 + -15 + -45x + 45x + 25x2 + -25x2

Combine like terms: 15 + -15 = 0
-15 + 45x + -25x2 = 0 + -45x + 45x + 25x2 + -25x2
-15 + 45x + -25x2 = -45x + 45x + 25x2 + -25x2

Combine like terms: -45x + 45x = 0
-15 + 45x + -25x2 = 0 + 25x2 + -25x2
-15 + 45x + -25x2 = 25x2 + -25x2

Combine like terms: 25x2 + -25x2 = 0
-15 + 45x + -25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + 9x + -5x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-3 + 9x + -5x2)' equal to zero and attempt to solve:

Simplifying
-3 + 9x + -5x2 = 0

Solving
-3 + 9x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.6 + -1.8x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -1.8x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -1.8x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -1.8x + x2 = 0 + -0.6
-1.8x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-1.8x + x2 = -0.6

The x term is -1.8x.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8x + 0.81 + x2 = -0.6 + 0.81

Reorder the terms:
0.81 + -1.8x + x2 = -0.6 + 0.81

Combine like terms: -0.6 + 0.81 = 0.21
0.81 + -1.8x + x2 = 0.21

Factor a perfect square on the left side:
(x + -0.9)(x + -0.9) = 0.21

Calculate the square root of the right side: 0.458257569

Break this problem into two subproblems by setting 
(x + -0.9) equal to 0.458257569 and -0.458257569.

Subproblem 1
x + -0.9 = 0.458257569

Simplifying
x + -0.9 = 0.458257569

Reorder the terms:
-0.9 + x = 0.458257569

Solving
-0.9 + x = 0.458257569

Solving for variable 'x'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + x = 0.458257569 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + x = 0.458257569 + 0.9
x = 0.458257569 + 0.9

Combine like terms: 0.458257569 + 0.9 = 1.358257569
x = 1.358257569

Simplifying
x = 1.358257569

Subproblem 2
x + -0.9 = -0.458257569

Simplifying
x + -0.9 = -0.458257569

Reorder the terms:
-0.9 + x = -0.458257569

Solving
-0.9 + x = -0.458257569

Solving for variable 'x'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + x = -0.458257569 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + x = -0.458257569 + 0.9
x = -0.458257569 + 0.9

Combine like terms: -0.458257569 + 0.9 = 0.441742431
x = 0.441742431

Simplifying
x = 0.441742431

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.358257569, 0.441742431}
Solution
x = {1.358257569, 0.441742431}