(3+x)(12+x)=3x

Solution for (3+x)(12+x)=3x equation:

Simplifying
(3 + x)(12 + x) = 3x

Multiply (3 + x) * (12 + x)
(3(12 + x) + x(12 + x)) = 3x
((12 * 3 + x * 3) + x(12 + x)) = 3x
((36 + 3x) + x(12 + x)) = 3x
(36 + 3x + (12 * x + x * x)) = 3x
(36 + 3x + (12x + x2)) = 3x

Combine like terms: 3x + 12x = 15x
(36 + 15x + x2) = 3x

Solving
36 + 15x + x2 = 3x

Solving for variable 'x'.

Reorder the terms:
36 + 15x + -3x + x2 = 3x + -3x

Combine like terms: 15x + -3x = 12x
36 + 12x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
36 + 12x + x2 = 0

Factor a trinomial.
(6 + x)(6 + x) = 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 '(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 = {-6, -6}