162=3(x+6)(x+3)

Solution for 162=3(x+6)(x+3) equation:

Simplifying
162 = 3(x + 6)(x + 3)

Reorder the terms:
162 = 3(6 + x)(x + 3)

Reorder the terms:
162 = 3(6 + x)(3 + x)

Multiply (6 + x) * (3 + x)
162 = 3(6(3 + x) + x(3 + x))
162 = 3((3 * 6 + x * 6) + x(3 + x))
162 = 3((18 + 6x) + x(3 + x))
162 = 3(18 + 6x + (3 * x + x * x))
162 = 3(18 + 6x + (3x + x2))

Combine like terms: 6x + 3x = 9x
162 = 3(18 + 9x + x2)
162 = (18 * 3 + 9x * 3 + x2 * 3)
162 = (54 + 27x + 3x2)

Solving
162 = 54 + 27x + 3x2

Solving for variable 'x'.

Combine like terms: 162 + -54 = 108
108 + -27x + -3x2 = 54 + 27x + 3x2 + -54 + -27x + -3x2

Reorder the terms:
108 + -27x + -3x2 = 54 + -54 + 27x + -27x + 3x2 + -3x2

Combine like terms: 54 + -54 = 0
108 + -27x + -3x2 = 0 + 27x + -27x + 3x2 + -3x2
108 + -27x + -3x2 = 27x + -27x + 3x2 + -3x2

Combine like terms: 27x + -27x = 0
108 + -27x + -3x2 = 0 + 3x2 + -3x2
108 + -27x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
108 + -27x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(36 + -9x + -1x2) = 0

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

Ignore the factor 3.
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 + 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
Solution
x = {3, -12}