(x-7)(x-9)-1(8x+9)(x+5)=

Solution for (x-7)(x-9)-1(8x+9)(x+5)= equation:

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

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

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

Multiply (-7 + x) * (-9 + x)
(-7(-9 + x) + x(-9 + x)) + -1(8x + 9)(x + 5) = 0
((-9 * -7 + x * -7) + x(-9 + x)) + -1(8x + 9)(x + 5) = 0
((63 + -7x) + x(-9 + x)) + -1(8x + 9)(x + 5) = 0
(63 + -7x + (-9 * x + x * x)) + -1(8x + 9)(x + 5) = 0
(63 + -7x + (-9x + x2)) + -1(8x + 9)(x + 5) = 0

Combine like terms: -7x + -9x = -16x
(63 + -16x + x2) + -1(8x + 9)(x + 5) = 0

Reorder the terms:
63 + -16x + x2 + -1(9 + 8x)(x + 5) = 0

Reorder the terms:
63 + -16x + x2 + -1(9 + 8x)(5 + x) = 0

Multiply (9 + 8x) * (5 + x)
63 + -16x + x2 + -1(9(5 + x) + 8x * (5 + x)) = 0
63 + -16x + x2 + -1((5 * 9 + x * 9) + 8x * (5 + x)) = 0
63 + -16x + x2 + -1((45 + 9x) + 8x * (5 + x)) = 0
63 + -16x + x2 + -1(45 + 9x + (5 * 8x + x * 8x)) = 0
63 + -16x + x2 + -1(45 + 9x + (40x + 8x2)) = 0

Combine like terms: 9x + 40x = 49x
63 + -16x + x2 + -1(45 + 49x + 8x2) = 0
63 + -16x + x2 + (45 * -1 + 49x * -1 + 8x2 * -1) = 0
63 + -16x + x2 + (-45 + -49x + -8x2) = 0

Reorder the terms:
63 + -45 + -16x + -49x + x2 + -8x2 = 0

Combine like terms: 63 + -45 = 18
18 + -16x + -49x + x2 + -8x2 = 0

Combine like terms: -16x + -49x = -65x
18 + -65x + x2 + -8x2 = 0

Combine like terms: x2 + -8x2 = -7x2
18 + -65x + -7x2 = 0

Solving
18 + -65x + -7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-2.571428571 + 9.285714286x + x2 = 0

Move the constant term to the right:

Add '2.571428571' to each side of the equation.
-2.571428571 + 9.285714286x + 2.571428571 + x2 = 0 + 2.571428571

Reorder the terms:
-2.571428571 + 2.571428571 + 9.285714286x + x2 = 0 + 2.571428571

Combine like terms: -2.571428571 + 2.571428571 = 0.000000000
0.000000000 + 9.285714286x + x2 = 0 + 2.571428571
9.285714286x + x2 = 0 + 2.571428571

Combine like terms: 0 + 2.571428571 = 2.571428571
9.285714286x + x2 = 2.571428571

The x term is 9.285714286x.  Take half its coefficient (4.642857143).
Square it (21.55612245) and add it to both sides.

Add '21.55612245' to each side of the equation.
9.285714286x + 21.55612245 + x2 = 2.571428571 + 21.55612245

Reorder the terms:
21.55612245 + 9.285714286x + x2 = 2.571428571 + 21.55612245

Combine like terms: 2.571428571 + 21.55612245 = 24.127551021
21.55612245 + 9.285714286x + x2 = 24.127551021

Factor a perfect square on the left side:
(x + 4.642857143)(x + 4.642857143) = 24.127551021

Calculate the square root of the right side: 4.911980356

Break this problem into two subproblems by setting 
(x + 4.642857143) equal to 4.911980356 and -4.911980356.

Subproblem 1
x + 4.642857143 = 4.911980356

Simplifying
x + 4.642857143 = 4.911980356

Reorder the terms:
4.642857143 + x = 4.911980356

Solving
4.642857143 + x = 4.911980356

Solving for variable 'x'.

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

Add '-4.642857143' to each side of the equation.
4.642857143 + -4.642857143 + x = 4.911980356 + -4.642857143

Combine like terms: 4.642857143 + -4.642857143 = 0.000000000
0.000000000 + x = 4.911980356 + -4.642857143
x = 4.911980356 + -4.642857143

Combine like terms: 4.911980356 + -4.642857143 = 0.269123213
x = 0.269123213

Simplifying
x = 0.269123213

Subproblem 2
x + 4.642857143 = -4.911980356

Simplifying
x + 4.642857143 = -4.911980356

Reorder the terms:
4.642857143 + x = -4.911980356

Solving
4.642857143 + x = -4.911980356

Solving for variable 'x'.

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

Add '-4.642857143' to each side of the equation.
4.642857143 + -4.642857143 + x = -4.911980356 + -4.642857143

Combine like terms: 4.642857143 + -4.642857143 = 0.000000000
0.000000000 + x = -4.911980356 + -4.642857143
x = -4.911980356 + -4.642857143

Combine like terms: -4.911980356 + -4.642857143 = -9.554837499
x = -9.554837499

Simplifying
x = -9.554837499

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.269123213, -9.554837499}