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

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


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

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

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

Multiply (2 + x) * (9 + x)
(2(9 + x) + x(9 + x)) + -1(5x + 3)(x + 7) = 0
((9 * 2 + x * 2) + x(9 + x)) + -1(5x + 3)(x + 7) = 0
((18 + 2x) + x(9 + x)) + -1(5x + 3)(x + 7) = 0
(18 + 2x + (9 * x + x * x)) + -1(5x + 3)(x + 7) = 0
(18 + 2x + (9x + x2)) + -1(5x + 3)(x + 7) = 0

Combine like terms: 2x + 9x = 11x
(18 + 11x + x2) + -1(5x + 3)(x + 7) = 0

Reorder the terms:
18 + 11x + x2 + -1(3 + 5x)(x + 7) = 0

Reorder the terms:
18 + 11x + x2 + -1(3 + 5x)(7 + x) = 0

Multiply (3 + 5x) * (7 + x)
18 + 11x + x2 + -1(3(7 + x) + 5x * (7 + x)) = 0
18 + 11x + x2 + -1((7 * 3 + x * 3) + 5x * (7 + x)) = 0
18 + 11x + x2 + -1((21 + 3x) + 5x * (7 + x)) = 0
18 + 11x + x2 + -1(21 + 3x + (7 * 5x + x * 5x)) = 0
18 + 11x + x2 + -1(21 + 3x + (35x + 5x2)) = 0

Combine like terms: 3x + 35x = 38x
18 + 11x + x2 + -1(21 + 38x + 5x2) = 0
18 + 11x + x2 + (21 * -1 + 38x * -1 + 5x2 * -1) = 0
18 + 11x + x2 + (-21 + -38x + -5x2) = 0

Reorder the terms:
18 + -21 + 11x + -38x + x2 + -5x2 = 0

Combine like terms: 18 + -21 = -3
-3 + 11x + -38x + x2 + -5x2 = 0

Combine like terms: 11x + -38x = -27x
-3 + -27x + x2 + -5x2 = 0

Combine like terms: x2 + -5x2 = -4x2
-3 + -27x + -4x2 = 0

Solving
-3 + -27x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 27x + 4x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(3 + 27x + 4x2)' equal to zero and attempt to solve:

Simplifying
3 + 27x + 4x2 = 0

Solving
3 + 27x + 4x2 = 0

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

Divide each side by '4'.
0.75 + 6.75x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 6.75x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 6.75x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 6.75x + x2 = 0 + -0.75
6.75x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
6.75x + x2 = -0.75

The x term is 6.75x.  Take half its coefficient (3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
6.75x + 11.390625 + x2 = -0.75 + 11.390625

Reorder the terms:
11.390625 + 6.75x + x2 = -0.75 + 11.390625

Combine like terms: -0.75 + 11.390625 = 10.640625
11.390625 + 6.75x + x2 = 10.640625

Factor a perfect square on the left side:
(x + 3.375)(x + 3.375) = 10.640625

Calculate the square root of the right side: 3.261997088

Break this problem into two subproblems by setting 
(x + 3.375) equal to 3.261997088 and -3.261997088.


Subproblem 1
x + 3.375 = 3.261997088

Simplifying
x + 3.375 = 3.261997088

Reorder the terms:
3.375 + x = 3.261997088

Solving
3.375 + x = 3.261997088

Solving for variable 'x'.

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

Add '-3.375' to each side of the equation.
3.375 + -3.375 + x = 3.261997088 + -3.375

Combine like terms: 3.375 + -3.375 = 0.000
0.000 + x = 3.261997088 + -3.375
x = 3.261997088 + -3.375

Combine like terms: 3.261997088 + -3.375 = -0.113002912
x = -0.113002912

Simplifying
x = -0.113002912


Subproblem 2
x + 3.375 = -3.261997088

Simplifying
x + 3.375 = -3.261997088

Reorder the terms:
3.375 + x = -3.261997088

Solving
3.375 + x = -3.261997088

Solving for variable 'x'.

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

Add '-3.375' to each side of the equation.
3.375 + -3.375 + x = -3.261997088 + -3.375

Combine like terms: 3.375 + -3.375 = 0.000
0.000 + x = -3.261997088 + -3.375
x = -3.261997088 + -3.375

Combine like terms: -3.261997088 + -3.375 = -6.636997088
x = -6.636997088

Simplifying
x = -6.636997088


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.113002912, -6.636997088}
Solution
x = {-0.113002912, -6.636997088}

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