(3+x)(x-12)=0

Solution for (3+x)(x-12)=0 equation:

Simplifying
(3 + x)(x + -12) = 0

Reorder the terms:
(3 + x)(-12 + x) = 0

Multiply (3 + x) * (-12 + x)
(3(-12 + x) + x(-12 + x)) = 0
((-12 * 3 + x * 3) + x(-12 + x)) = 0
((-36 + 3x) + x(-12 + x)) = 0
(-36 + 3x + (-12 * x + x * x)) = 0
(-36 + 3x + (-12x + x2)) = 0

Combine like terms: 3x + -12x = -9x
(-36 + -9x + x2) = 0

Solving
-36 + -9x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x)(12 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-3, 12}