0=12((x-3)(x+7))

Solution for 0=12((x-3)(x+7)) equation:

Simplifying
0 = 12((x + -3)(x + 7))

Reorder the terms:
0 = 12((-3 + x)(x + 7))

Reorder the terms:
0 = 12((-3 + x)(7 + x))

Multiply (-3 + x) * (7 + x)
0 = 12((-3(7 + x) + x(7 + x)))
0 = 12(((7 * -3 + x * -3) + x(7 + x)))
0 = 12(((-21 + -3x) + x(7 + x)))
0 = 12((-21 + -3x + (7 * x + x * x)))
0 = 12((-21 + -3x + (7x + x2)))

Combine like terms: -3x + 7x = 4x
0 = 12((-21 + 4x + x2))
0 = (-21 * 12 + 4x * 12 + x2 * 12)
0 = (-252 + 48x + 12x2)

Solving
0 = -252 + 48x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + 252 = 252
252 + -48x + -12x2 = -252 + 48x + 12x2 + 252 + -48x + -12x2

Reorder the terms:
252 + -48x + -12x2 = -252 + 252 + 48x + -48x + 12x2 + -12x2

Combine like terms: -252 + 252 = 0
252 + -48x + -12x2 = 0 + 48x + -48x + 12x2 + -12x2
252 + -48x + -12x2 = 48x + -48x + 12x2 + -12x2

Combine like terms: 48x + -48x = 0
252 + -48x + -12x2 = 0 + 12x2 + -12x2
252 + -48x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
252 + -48x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(21 + -4x + -1x2) = 0

Factor a trinomial.
12((3 + -1x)(7 + x)) = 0

Ignore the factor 12.
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 '(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
Solution
x = {3, -7}