(x+6)(x+3)=40

Solution for (x+6)(x+3)=40 equation:

Simplifying
(x + 6)(x + 3) = 40

Reorder the terms:
(6 + x)(x + 3) = 40

Reorder the terms:
(6 + x)(3 + x) = 40

Multiply (6 + x) * (3 + x)
(6(3 + x) + x(3 + x)) = 40
((3 * 6 + x * 6) + x(3 + x)) = 40
((18 + 6x) + x(3 + x)) = 40
(18 + 6x + (3 * x + x * x)) = 40
(18 + 6x + (3x + x2)) = 40

Combine like terms: 6x + 3x = 9x
(18 + 9x + x2) = 40

Solving
18 + 9x + x2 = 40

Solving for variable 'x'.

Reorder the terms:
18 + -40 + 9x + x2 = 40 + -40

Combine like terms: 18 + -40 = -22
-22 + 9x + x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-22 + 9x + x2 = 0

Factor a trinomial.
(-11 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-11, 2}