240=(3x+9)(x+5)

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Solution for 240=(3x+9)(x+5) equation: 


Simplifying
240 = (3x + 9)(x + 5)

Reorder the terms:
240 = (9 + 3x)(x + 5)

Reorder the terms:
240 = (9 + 3x)(5 + x)

Multiply (9 + 3x) * (5 + x)
240 = (9(5 + x) + 3x * (5 + x))
240 = ((5 * 9 + x * 9) + 3x * (5 + x))
240 = ((45 + 9x) + 3x * (5 + x))
240 = (45 + 9x + (5 * 3x + x * 3x))
240 = (45 + 9x + (15x + 3x2))

Combine like terms: 9x + 15x = 24x
240 = (45 + 24x + 3x2)

Solving
240 = 45 + 24x + 3x2

Solving for variable 'x'.

Combine like terms: 240 + -45 = 195
195 + -24x + -3x2 = 45 + 24x + 3x2 + -45 + -24x + -3x2

Reorder the terms:
195 + -24x + -3x2 = 45 + -45 + 24x + -24x + 3x2 + -3x2

Combine like terms: 45 + -45 = 0
195 + -24x + -3x2 = 0 + 24x + -24x + 3x2 + -3x2
195 + -24x + -3x2 = 24x + -24x + 3x2 + -3x2

Combine like terms: 24x + -24x = 0
195 + -24x + -3x2 = 0 + 3x2 + -3x2
195 + -24x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
195 + -24x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(65 + -8x + -1x2) = 0

Factor a trinomial.
3((5 + -1x)(13 + x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(13 + x)' equal to zero and attempt to solve:

Simplifying
13 + x = 0

Solving
13 + x = 0

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

Add '-13' to each side of the equation.
13 + -13 + x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + x = 0 + -13
x = 0 + -13

Combine like terms: 0 + -13 = -13
x = -13

Simplifying
x = -13
Solution
x = {5, -13}

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