(4x-7)(5x-6)-(9x-5)(8x-5)=0

Solution for (4x-7)(5x-6)-(9x-5)(8x-5)=0 equation:

Simplifying
(4x + -7)(5x + -6) + -1(9x + -5)(8x + -5) = 0

Reorder the terms:
(-7 + 4x)(5x + -6) + -1(9x + -5)(8x + -5) = 0

Reorder the terms:
(-7 + 4x)(-6 + 5x) + -1(9x + -5)(8x + -5) = 0

Multiply (-7 + 4x) * (-6 + 5x)
(-7(-6 + 5x) + 4x * (-6 + 5x)) + -1(9x + -5)(8x + -5) = 0
((-6 * -7 + 5x * -7) + 4x * (-6 + 5x)) + -1(9x + -5)(8x + -5) = 0
((42 + -35x) + 4x * (-6 + 5x)) + -1(9x + -5)(8x + -5) = 0
(42 + -35x + (-6 * 4x + 5x * 4x)) + -1(9x + -5)(8x + -5) = 0
(42 + -35x + (-24x + 20x2)) + -1(9x + -5)(8x + -5) = 0

Combine like terms: -35x + -24x = -59x
(42 + -59x + 20x2) + -1(9x + -5)(8x + -5) = 0

Reorder the terms:
42 + -59x + 20x2 + -1(-5 + 9x)(8x + -5) = 0

Reorder the terms:
42 + -59x + 20x2 + -1(-5 + 9x)(-5 + 8x) = 0

Multiply (-5 + 9x) * (-5 + 8x)
42 + -59x + 20x2 + -1(-5(-5 + 8x) + 9x * (-5 + 8x)) = 0
42 + -59x + 20x2 + -1((-5 * -5 + 8x * -5) + 9x * (-5 + 8x)) = 0
42 + -59x + 20x2 + -1((25 + -40x) + 9x * (-5 + 8x)) = 0
42 + -59x + 20x2 + -1(25 + -40x + (-5 * 9x + 8x * 9x)) = 0
42 + -59x + 20x2 + -1(25 + -40x + (-45x + 72x2)) = 0

Combine like terms: -40x + -45x = -85x
42 + -59x + 20x2 + -1(25 + -85x + 72x2) = 0
42 + -59x + 20x2 + (25 * -1 + -85x * -1 + 72x2 * -1) = 0
42 + -59x + 20x2 + (-25 + 85x + -72x2) = 0

Reorder the terms:
42 + -25 + -59x + 85x + 20x2 + -72x2 = 0

Combine like terms: 42 + -25 = 17
17 + -59x + 85x + 20x2 + -72x2 = 0

Combine like terms: -59x + 85x = 26x
17 + 26x + 20x2 + -72x2 = 0

Combine like terms: 20x2 + -72x2 = -52x2
17 + 26x + -52x2 = 0

Solving
17 + 26x + -52x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-52 the coefficient of the squared term: 

Divide each side by '-52'.
-0.3269230769 + -0.5x + x2 = 0

Move the constant term to the right:

Add '0.3269230769' to each side of the equation.
-0.3269230769 + -0.5x + 0.3269230769 + x2 = 0 + 0.3269230769

Reorder the terms:
-0.3269230769 + 0.3269230769 + -0.5x + x2 = 0 + 0.3269230769

Combine like terms: -0.3269230769 + 0.3269230769 = 0.0000000000
0.0000000000 + -0.5x + x2 = 0 + 0.3269230769
-0.5x + x2 = 0 + 0.3269230769

Combine like terms: 0 + 0.3269230769 = 0.3269230769
-0.5x + x2 = 0.3269230769

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.3269230769 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.3269230769 + 0.0625

Combine like terms: 0.3269230769 + 0.0625 = 0.3894230769
0.0625 + -0.5x + x2 = 0.3894230769

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.3894230769

Calculate the square root of the right side: 0.624037721

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.624037721 and -0.624037721.

Subproblem 1
x + -0.25 = 0.624037721

Simplifying
x + -0.25 = 0.624037721

Reorder the terms:
-0.25 + x = 0.624037721

Solving
-0.25 + x = 0.624037721

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 0.624037721 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 0.624037721 + 0.25
x = 0.624037721 + 0.25

Combine like terms: 0.624037721 + 0.25 = 0.874037721
x = 0.874037721

Simplifying
x = 0.874037721

Subproblem 2
x + -0.25 = -0.624037721

Simplifying
x + -0.25 = -0.624037721

Reorder the terms:
-0.25 + x = -0.624037721

Solving
-0.25 + x = -0.624037721

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -0.624037721 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -0.624037721 + 0.25
x = -0.624037721 + 0.25

Combine like terms: -0.624037721 + 0.25 = -0.374037721
x = -0.374037721

Simplifying
x = -0.374037721

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.874037721, -0.374037721}