(x-1)(x-4)-(2x+5)(8x-3)=

Solution for (x-1)(x-4)-(2x+5)(8x-3)= equation:

Simplifying
(x + -1)(x + -4) + -1(2x + 5)(8x + -3) = 0

Reorder the terms:
(-1 + x)(x + -4) + -1(2x + 5)(8x + -3) = 0

Reorder the terms:
(-1 + x)(-4 + x) + -1(2x + 5)(8x + -3) = 0

Multiply (-1 + x) * (-4 + x)
(-1(-4 + x) + x(-4 + x)) + -1(2x + 5)(8x + -3) = 0
((-4 * -1 + x * -1) + x(-4 + x)) + -1(2x + 5)(8x + -3) = 0
((4 + -1x) + x(-4 + x)) + -1(2x + 5)(8x + -3) = 0
(4 + -1x + (-4 * x + x * x)) + -1(2x + 5)(8x + -3) = 0
(4 + -1x + (-4x + x2)) + -1(2x + 5)(8x + -3) = 0

Combine like terms: -1x + -4x = -5x
(4 + -5x + x2) + -1(2x + 5)(8x + -3) = 0

Reorder the terms:
4 + -5x + x2 + -1(5 + 2x)(8x + -3) = 0

Reorder the terms:
4 + -5x + x2 + -1(5 + 2x)(-3 + 8x) = 0

Multiply (5 + 2x) * (-3 + 8x)
4 + -5x + x2 + -1(5(-3 + 8x) + 2x * (-3 + 8x)) = 0
4 + -5x + x2 + -1((-3 * 5 + 8x * 5) + 2x * (-3 + 8x)) = 0
4 + -5x + x2 + -1((-15 + 40x) + 2x * (-3 + 8x)) = 0
4 + -5x + x2 + -1(-15 + 40x + (-3 * 2x + 8x * 2x)) = 0
4 + -5x + x2 + -1(-15 + 40x + (-6x + 16x2)) = 0

Combine like terms: 40x + -6x = 34x
4 + -5x + x2 + -1(-15 + 34x + 16x2) = 0
4 + -5x + x2 + (-15 * -1 + 34x * -1 + 16x2 * -1) = 0
4 + -5x + x2 + (15 + -34x + -16x2) = 0

Reorder the terms:
4 + 15 + -5x + -34x + x2 + -16x2 = 0

Combine like terms: 4 + 15 = 19
19 + -5x + -34x + x2 + -16x2 = 0

Combine like terms: -5x + -34x = -39x
19 + -39x + x2 + -16x2 = 0

Combine like terms: x2 + -16x2 = -15x2
19 + -39x + -15x2 = 0

Solving
19 + -39x + -15x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
-1.266666667 + 2.6x + x2 = 0

Move the constant term to the right:

Add '1.266666667' to each side of the equation.
-1.266666667 + 2.6x + 1.266666667 + x2 = 0 + 1.266666667

Reorder the terms:
-1.266666667 + 1.266666667 + 2.6x + x2 = 0 + 1.266666667

Combine like terms: -1.266666667 + 1.266666667 = 0.000000000
0.000000000 + 2.6x + x2 = 0 + 1.266666667
2.6x + x2 = 0 + 1.266666667

Combine like terms: 0 + 1.266666667 = 1.266666667
2.6x + x2 = 1.266666667

The x term is 2.6x.  Take half its coefficient (1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
2.6x + 1.69 + x2 = 1.266666667 + 1.69

Reorder the terms:
1.69 + 2.6x + x2 = 1.266666667 + 1.69

Combine like terms: 1.266666667 + 1.69 = 2.956666667
1.69 + 2.6x + x2 = 2.956666667

Factor a perfect square on the left side:
(x + 1.3)(x + 1.3) = 2.956666667

Calculate the square root of the right side: 1.71949605

Break this problem into two subproblems by setting 
(x + 1.3) equal to 1.71949605 and -1.71949605.

Subproblem 1
x + 1.3 = 1.71949605

Simplifying
x + 1.3 = 1.71949605

Reorder the terms:
1.3 + x = 1.71949605

Solving
1.3 + x = 1.71949605

Solving for variable 'x'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + x = 1.71949605 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + x = 1.71949605 + -1.3
x = 1.71949605 + -1.3

Combine like terms: 1.71949605 + -1.3 = 0.41949605
x = 0.41949605

Simplifying
x = 0.41949605

Subproblem 2
x + 1.3 = -1.71949605

Simplifying
x + 1.3 = -1.71949605

Reorder the terms:
1.3 + x = -1.71949605

Solving
1.3 + x = -1.71949605

Solving for variable 'x'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + x = -1.71949605 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + x = -1.71949605 + -1.3
x = -1.71949605 + -1.3

Combine like terms: -1.71949605 + -1.3 = -3.01949605
x = -3.01949605

Simplifying
x = -3.01949605

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.41949605, -3.01949605}