(x+3)(x+4)+(x+6)(x-3)=

Solution for (x+3)(x+4)+(x+6)(x-3)= equation:

Simplifying
(x + 3)(x + 4) + (x + 6)(x + -3) = 0

Reorder the terms:
(3 + x)(x + 4) + (x + 6)(x + -3) = 0

Reorder the terms:
(3 + x)(4 + x) + (x + 6)(x + -3) = 0

Multiply (3 + x) * (4 + x)
(3(4 + x) + x(4 + x)) + (x + 6)(x + -3) = 0
((4 * 3 + x * 3) + x(4 + x)) + (x + 6)(x + -3) = 0
((12 + 3x) + x(4 + x)) + (x + 6)(x + -3) = 0
(12 + 3x + (4 * x + x * x)) + (x + 6)(x + -3) = 0
(12 + 3x + (4x + x2)) + (x + 6)(x + -3) = 0

Combine like terms: 3x + 4x = 7x
(12 + 7x + x2) + (x + 6)(x + -3) = 0

Reorder the terms:
12 + 7x + x2 + (6 + x)(x + -3) = 0

Reorder the terms:
12 + 7x + x2 + (6 + x)(-3 + x) = 0

Multiply (6 + x) * (-3 + x)
12 + 7x + x2 + (6(-3 + x) + x(-3 + x)) = 0
12 + 7x + x2 + ((-3 * 6 + x * 6) + x(-3 + x)) = 0
12 + 7x + x2 + ((-18 + 6x) + x(-3 + x)) = 0
12 + 7x + x2 + (-18 + 6x + (-3 * x + x * x)) = 0
12 + 7x + x2 + (-18 + 6x + (-3x + x2)) = 0

Combine like terms: 6x + -3x = 3x
12 + 7x + x2 + (-18 + 3x + x2) = 0

Reorder the terms:
12 + -18 + 7x + 3x + x2 + x2 = 0

Combine like terms: 12 + -18 = -6
-6 + 7x + 3x + x2 + x2 = 0

Combine like terms: 7x + 3x = 10x
-6 + 10x + x2 + x2 = 0

Combine like terms: x2 + x2 = 2x2
-6 + 10x + 2x2 = 0

Solving
-6 + 10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 5x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-3 + 5x + x2 = 0

Solving
-3 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 5x + 3 + x2 = 0 + 3

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

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

Combine like terms: 0 + 3 = 3
5x + x2 = 3

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 3 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 3 + 6.25

Combine like terms: 3 + 6.25 = 9.25
6.25 + 5x + x2 = 9.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.041381265 and -3.041381265.

Subproblem 1
x + 2.5 = 3.041381265

Simplifying
x + 2.5 = 3.041381265

Reorder the terms:
2.5 + x = 3.041381265

Solving
2.5 + x = 3.041381265

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3.041381265 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.041381265 + -2.5
x = 3.041381265 + -2.5

Combine like terms: 3.041381265 + -2.5 = 0.541381265
x = 0.541381265

Simplifying
x = 0.541381265

Subproblem 2
x + 2.5 = -3.041381265

Simplifying
x + 2.5 = -3.041381265

Reorder the terms:
2.5 + x = -3.041381265

Solving
2.5 + x = -3.041381265

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3.041381265 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.041381265 + -2.5
x = -3.041381265 + -2.5

Combine like terms: -3.041381265 + -2.5 = -5.541381265
x = -5.541381265

Simplifying
x = -5.541381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.541381265, -5.541381265}
Solution
x = {0.541381265, -5.541381265}