(7x+6)+x(7x+6)=0

Solution for (7x+6)+x(7x+6)=0 equation:

Simplifying
(7x + 6) + x(7x + 6) = 0

Reorder the terms:
(6 + 7x) + x(7x + 6) = 0

Remove parenthesis around (6 + 7x)
6 + 7x + x(7x + 6) = 0

Reorder the terms:
6 + 7x + x(6 + 7x) = 0
6 + 7x + (6 * x + 7x * x) = 0
6 + 7x + (6x + 7x2) = 0

Combine like terms: 7x + 6x = 13x
6 + 13x + 7x2 = 0

Solving
6 + 13x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + x)(6 + 7x) = 0

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(6 + 7x)' equal to zero and attempt to solve:

Simplifying
6 + 7x = 0

Solving
6 + 7x = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7x = 0 + -6
7x = 0 + -6

Combine like terms: 0 + -6 = -6
7x = -6

Divide each side by '7'.
x = -0.8571428571

Simplifying
x = -0.8571428571
Solution
x = {-1, -0.8571428571}