(x+1)(x+6)=36

Solution for (x+1)(x+6)=36 equation:

Simplifying
(x + 1)(x + 6) = 36

Reorder the terms:
(1 + x)(x + 6) = 36

Reorder the terms:
(1 + x)(6 + x) = 36

Multiply (1 + x) * (6 + x)
(1(6 + x) + x(6 + x)) = 36
((6 * 1 + x * 1) + x(6 + x)) = 36
((6 + 1x) + x(6 + x)) = 36
(6 + 1x + (6 * x + x * x)) = 36
(6 + 1x + (6x + x2)) = 36

Combine like terms: 1x + 6x = 7x
(6 + 7x + x2) = 36

Solving
6 + 7x + x2 = 36

Solving for variable 'x'.

Reorder the terms:
6 + -36 + 7x + x2 = 36 + -36

Combine like terms: 6 + -36 = -30
-30 + 7x + x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-30 + 7x + x2 = 0

Factor a trinomial.
(-10 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-10, 3}