(x+6)(x+1)=50

Solution for (x+6)(x+1)=50 equation:

Simplifying
(x + 6)(x + 1) = 50

Reorder the terms:
(6 + x)(x + 1) = 50

Reorder the terms:
(6 + x)(1 + x) = 50

Multiply (6 + x) * (1 + x)
(6(1 + x) + x(1 + x)) = 50
((1 * 6 + x * 6) + x(1 + x)) = 50
((6 + 6x) + x(1 + x)) = 50
(6 + 6x + (1 * x + x * x)) = 50
(6 + 6x + (1x + x2)) = 50

Combine like terms: 6x + 1x = 7x
(6 + 7x + x2) = 50

Solving
6 + 7x + x2 = 50

Solving for variable 'x'.

Reorder the terms:
6 + -50 + 7x + x2 = 50 + -50

Combine like terms: 6 + -50 = -44
-44 + 7x + x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-44 + 7x + x2 = 0

Factor a trinomial.
(-11 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-11, 4}