(x+1)(x+6)=126

Solution for (x+1)(x+6)=126 equation:

Simplifying
(x + 1)(x + 6) = 126

Reorder the terms:
(1 + x)(x + 6) = 126

Reorder the terms:
(1 + x)(6 + x) = 126

Multiply (1 + x) * (6 + x)
(1(6 + x) + x(6 + x)) = 126
((6 * 1 + x * 1) + x(6 + x)) = 126
((6 + 1x) + x(6 + x)) = 126
(6 + 1x + (6 * x + x * x)) = 126
(6 + 1x + (6x + x2)) = 126

Combine like terms: 1x + 6x = 7x
(6 + 7x + x2) = 126

Solving
6 + 7x + x2 = 126

Solving for variable 'x'.

Reorder the terms:
6 + -126 + 7x + x2 = 126 + -126

Combine like terms: 6 + -126 = -120
-120 + 7x + x2 = 126 + -126

Combine like terms: 126 + -126 = 0
-120 + 7x + x2 = 0

Factor a trinomial.
(-15 + -1x)(8 + -1x) = 0

Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-15, 8}