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

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

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

Reorder the terms:
x(10 + x) = -7(6 + x)
(10 * x + x * x) = -7(6 + x)
(10x + x2) = -7(6 + x)
10x + x2 = (6 * -7 + x * -7)
10x + x2 = (-42 + -7x)

Solving
10x + x2 = -42 + -7x

Solving for variable 'x'.

Reorder the terms:
42 + 10x + 7x + x2 = -42 + -7x + 42 + 7x

Combine like terms: 10x + 7x = 17x
42 + 17x + x2 = -42 + -7x + 42 + 7x

Reorder the terms:
42 + 17x + x2 = -42 + 42 + -7x + 7x

Combine like terms: -42 + 42 = 0
42 + 17x + x2 = 0 + -7x + 7x
42 + 17x + x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
42 + 17x + x2 = 0

Factor a trinomial.
(14 + x)(3 + x) = 0

Subproblem 1
Set the factor '(14 + x)' equal to zero and attempt to solve:

Simplifying
14 + x = 0

Solving
14 + x = 0

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

Add '-14' to each side of the equation.
14 + -14 + x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + x = 0 + -14
x = 0 + -14

Combine like terms: 0 + -14 = -14
x = -14

Simplifying
x = -14
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-14, -3}