=(x+3)(x+12)

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

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

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

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

Multiply (3 + x) * (12 + x)
0 = (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))

Combine like terms: 3x + 12x = 15x
0 = (36 + 15x + x2)

Solving
0 = 36 + 15x + x2

Solving for variable 'x'.

Combine like terms: 0 + -36 = -36
-36 + -15x + -1x2 = 36 + 15x + x2 + -36 + -15x + -1x2

Reorder the terms:
-36 + -15x + -1x2 = 36 + -36 + 15x + -15x + x2 + -1x2

Combine like terms: 36 + -36 = 0
-36 + -15x + -1x2 = 0 + 15x + -15x + x2 + -1x2
-36 + -15x + -1x2 = 15x + -15x + x2 + -1x2

Combine like terms: 15x + -15x = 0
-36 + -15x + -1x2 = 0 + x2 + -1x2
-36 + -15x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + -15x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(36 + 15x + x2) = 0

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

Ignore the factor -1.
Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 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 + x = 0 + -12

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

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

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