240=(x+2)(3x+12)

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Solution for 240=(x+2)(3x+12) equation: 


Simplifying
240 = (x + 2)(3x + 12)

Reorder the terms:
240 = (2 + x)(3x + 12)

Reorder the terms:
240 = (2 + x)(12 + 3x)

Multiply (2 + x) * (12 + 3x)
240 = (2(12 + 3x) + x(12 + 3x))
240 = ((12 * 2 + 3x * 2) + x(12 + 3x))
240 = ((24 + 6x) + x(12 + 3x))
240 = (24 + 6x + (12 * x + 3x * x))
240 = (24 + 6x + (12x + 3x2))

Combine like terms: 6x + 12x = 18x
240 = (24 + 18x + 3x2)

Solving
240 = 24 + 18x + 3x2

Solving for variable 'x'.

Combine like terms: 240 + -24 = 216
216 + -18x + -3x2 = 24 + 18x + 3x2 + -24 + -18x + -3x2

Reorder the terms:
216 + -18x + -3x2 = 24 + -24 + 18x + -18x + 3x2 + -3x2

Combine like terms: 24 + -24 = 0
216 + -18x + -3x2 = 0 + 18x + -18x + 3x2 + -3x2
216 + -18x + -3x2 = 18x + -18x + 3x2 + -3x2

Combine like terms: 18x + -18x = 0
216 + -18x + -3x2 = 0 + 3x2 + -3x2
216 + -18x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
216 + -18x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(72 + -6x + -1x2) = 0

Factor a trinomial.
3((6 + -1x)(12 + x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

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 = {6, -12}

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