(x+6)(7x+10)=0

Solution for (x+6)(7x+10)=0 equation:

Simplifying
(x + 6)(7x + 10) = 0

Reorder the terms:
(6 + x)(7x + 10) = 0

Reorder the terms:
(6 + x)(10 + 7x) = 0

Multiply (6 + x) * (10 + 7x)
(6(10 + 7x) + x(10 + 7x)) = 0
((10 * 6 + 7x * 6) + x(10 + 7x)) = 0
((60 + 42x) + x(10 + 7x)) = 0
(60 + 42x + (10 * x + 7x * x)) = 0
(60 + 42x + (10x + 7x2)) = 0

Combine like terms: 42x + 10x = 52x
(60 + 52x + 7x2) = 0

Solving
60 + 52x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + x)(10 + 7x) = 0

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Subproblem 2
Set the factor '(10 + 7x)' equal to zero and attempt to solve:

Simplifying
10 + 7x = 0

Solving
10 + 7x = 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 + 7x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 7x = 0 + -10
7x = 0 + -10

Combine like terms: 0 + -10 = -10
7x = -10

Divide each side by '7'.
x = -1.428571429

Simplifying
x = -1.428571429
Solution
x = {-6, -1.428571429}