(x+3)(x-9)-(-5x-7)(x-2)=

Solution for (x+3)(x-9)-(-5x-7)(x-2)= equation:

Simplifying
(x + 3)(x + -9) + -1(-5x + -7)(x + -2) = 0

Reorder the terms:
(3 + x)(x + -9) + -1(-5x + -7)(x + -2) = 0

Reorder the terms:
(3 + x)(-9 + x) + -1(-5x + -7)(x + -2) = 0

Multiply (3 + x) * (-9 + x)
(3(-9 + x) + x(-9 + x)) + -1(-5x + -7)(x + -2) = 0
((-9 * 3 + x * 3) + x(-9 + x)) + -1(-5x + -7)(x + -2) = 0
((-27 + 3x) + x(-9 + x)) + -1(-5x + -7)(x + -2) = 0
(-27 + 3x + (-9 * x + x * x)) + -1(-5x + -7)(x + -2) = 0
(-27 + 3x + (-9x + x2)) + -1(-5x + -7)(x + -2) = 0

Combine like terms: 3x + -9x = -6x
(-27 + -6x + x2) + -1(-5x + -7)(x + -2) = 0

Reorder the terms:
-27 + -6x + x2 + -1(-7 + -5x)(x + -2) = 0

Reorder the terms:
-27 + -6x + x2 + -1(-7 + -5x)(-2 + x) = 0

Multiply (-7 + -5x) * (-2 + x)
-27 + -6x + x2 + -1(-7(-2 + x) + -5x * (-2 + x)) = 0
-27 + -6x + x2 + -1((-2 * -7 + x * -7) + -5x * (-2 + x)) = 0
-27 + -6x + x2 + -1((14 + -7x) + -5x * (-2 + x)) = 0
-27 + -6x + x2 + -1(14 + -7x + (-2 * -5x + x * -5x)) = 0
-27 + -6x + x2 + -1(14 + -7x + (10x + -5x2)) = 0

Combine like terms: -7x + 10x = 3x
-27 + -6x + x2 + -1(14 + 3x + -5x2) = 0
-27 + -6x + x2 + (14 * -1 + 3x * -1 + -5x2 * -1) = 0
-27 + -6x + x2 + (-14 + -3x + 5x2) = 0

Reorder the terms:
-27 + -14 + -6x + -3x + x2 + 5x2 = 0

Combine like terms: -27 + -14 = -41
-41 + -6x + -3x + x2 + 5x2 = 0

Combine like terms: -6x + -3x = -9x
-41 + -9x + x2 + 5x2 = 0

Combine like terms: x2 + 5x2 = 6x2
-41 + -9x + 6x2 = 0

Solving
-41 + -9x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-6.833333333 + -1.5x + x2 = 0

Move the constant term to the right:

Add '6.833333333' to each side of the equation.
-6.833333333 + -1.5x + 6.833333333 + x2 = 0 + 6.833333333

Reorder the terms:
-6.833333333 + 6.833333333 + -1.5x + x2 = 0 + 6.833333333

Combine like terms: -6.833333333 + 6.833333333 = 0.000000000
0.000000000 + -1.5x + x2 = 0 + 6.833333333
-1.5x + x2 = 0 + 6.833333333

Combine like terms: 0 + 6.833333333 = 6.833333333
-1.5x + x2 = 6.833333333

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 6.833333333 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 6.833333333 + 0.5625

Combine like terms: 6.833333333 + 0.5625 = 7.395833333
0.5625 + -1.5x + x2 = 7.395833333

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 7.395833333

Calculate the square root of the right side: 2.719528145

Break this problem into two subproblems by setting 
(x + -0.75) equal to 2.719528145 and -2.719528145.

Subproblem 1
x + -0.75 = 2.719528145

Simplifying
x + -0.75 = 2.719528145

Reorder the terms:
-0.75 + x = 2.719528145

Solving
-0.75 + x = 2.719528145

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 2.719528145 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 2.719528145 + 0.75
x = 2.719528145 + 0.75

Combine like terms: 2.719528145 + 0.75 = 3.469528145
x = 3.469528145

Simplifying
x = 3.469528145

Subproblem 2
x + -0.75 = -2.719528145

Simplifying
x + -0.75 = -2.719528145

Reorder the terms:
-0.75 + x = -2.719528145

Solving
-0.75 + x = -2.719528145

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -2.719528145 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -2.719528145 + 0.75
x = -2.719528145 + 0.75

Combine like terms: -2.719528145 + 0.75 = -1.969528145
x = -1.969528145

Simplifying
x = -1.969528145

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.469528145, -1.969528145}