12(x+7)=-2x(x+7)

Solution for 12(x+7)=-2x(x+7) equation:

Simplifying
12(x + 7) = -2x(x + 7)

Reorder the terms:
12(7 + x) = -2x(x + 7)
(7 * 12 + x * 12) = -2x(x + 7)
(84 + 12x) = -2x(x + 7)

Reorder the terms:
84 + 12x = -2x(7 + x)
84 + 12x = (7 * -2x + x * -2x)
84 + 12x = (-14x + -2x2)

Solving
84 + 12x = -14x + -2x2

Solving for variable 'x'.

Combine like terms: 12x + 14x = 26x
84 + 26x + 2x2 = -14x + -2x2 + 14x + 2x2

Reorder the terms:
84 + 26x + 2x2 = -14x + 14x + -2x2 + 2x2

Combine like terms: -14x + 14x = 0
84 + 26x + 2x2 = 0 + -2x2 + 2x2
84 + 26x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
84 + 26x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(42 + 13x + x2) = 0

Factor a trinomial.
2((7 + x)(6 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

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

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

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

Simplifying
x = -7
Subproblem 2
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
Solution
x = {-7, -6}