(x+6)(x+1)=14

Solution for (x+6)(x+1)=14 equation:

Simplifying
(x + 6)(x + 1) = 14

Reorder the terms:
(6 + x)(x + 1) = 14

Reorder the terms:
(6 + x)(1 + x) = 14

Multiply (6 + x) * (1 + x)
(6(1 + x) + x(1 + x)) = 14
((1 * 6 + x * 6) + x(1 + x)) = 14
((6 + 6x) + x(1 + x)) = 14
(6 + 6x + (1 * x + x * x)) = 14
(6 + 6x + (1x + x2)) = 14

Combine like terms: 6x + 1x = 7x
(6 + 7x + x2) = 14

Solving
6 + 7x + x2 = 14

Solving for variable 'x'.

Reorder the terms:
6 + -14 + 7x + x2 = 14 + -14

Combine like terms: 6 + -14 = -8
-8 + 7x + x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-8 + 7x + x2 = 0

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-8, 1}