(x+6)(x+3)=340

Solution for (x+6)(x+3)=340 equation:

Simplifying
(x + 6)(x + 3) = 340

Reorder the terms:
(6 + x)(x + 3) = 340

Reorder the terms:
(6 + x)(3 + x) = 340

Multiply (6 + x) * (3 + x)
(6(3 + x) + x(3 + x)) = 340
((3 * 6 + x * 6) + x(3 + x)) = 340
((18 + 6x) + x(3 + x)) = 340
(18 + 6x + (3 * x + x * x)) = 340
(18 + 6x + (3x + x2)) = 340

Combine like terms: 6x + 3x = 9x
(18 + 9x + x2) = 340

Solving
18 + 9x + x2 = 340

Solving for variable 'x'.

Reorder the terms:
18 + -340 + 9x + x2 = 340 + -340

Combine like terms: 18 + -340 = -322
-322 + 9x + x2 = 340 + -340

Combine like terms: 340 + -340 = 0
-322 + 9x + x2 = 0

Factor a trinomial.
(-23 + -1x)(14 + -1x) = 0

Subproblem 1
Set the factor '(-23 + -1x)' equal to zero and attempt to solve:

Simplifying
-23 + -1x = 0

Solving
-23 + -1x = 0

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

Add '23' to each side of the equation.
-23 + 23 + -1x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -1x = 0 + 23
-1x = 0 + 23

Combine like terms: 0 + 23 = 23
-1x = 23

Divide each side by '-1'.
x = -23

Simplifying
x = -23
Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {-23, 14}