(x+6)+(8(x+3))=3(x+6)(x+3)

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Solution for (x+6)+(8(x+3))=3(x+6)(x+3) equation: 


Simplifying
(x + 6) + (8(x + 3)) = 3(x + 6)(x + 3)

Reorder the terms:
(6 + x) + (8(x + 3)) = 3(x + 6)(x + 3)

Remove parenthesis around (6 + x)
6 + x + (8(x + 3)) = 3(x + 6)(x + 3)

Reorder the terms:
6 + x + (8(3 + x)) = 3(x + 6)(x + 3)
6 + x + ((3 * 8 + x * 8)) = 3(x + 6)(x + 3)
6 + x + ((24 + 8x)) = 3(x + 6)(x + 3)
6 + x + (24 + 8x) = 3(x + 6)(x + 3)

Remove parenthesis around (24 + 8x)
6 + x + 24 + 8x = 3(x + 6)(x + 3)

Reorder the terms:
6 + 24 + x + 8x = 3(x + 6)(x + 3)

Combine like terms: 6 + 24 = 30
30 + x + 8x = 3(x + 6)(x + 3)

Combine like terms: x + 8x = 9x
30 + 9x = 3(x + 6)(x + 3)

Reorder the terms:
30 + 9x = 3(6 + x)(x + 3)

Reorder the terms:
30 + 9x = 3(6 + x)(3 + x)

Multiply (6 + x) * (3 + x)
30 + 9x = 3(6(3 + x) + x(3 + x))
30 + 9x = 3((3 * 6 + x * 6) + x(3 + x))
30 + 9x = 3((18 + 6x) + x(3 + x))
30 + 9x = 3(18 + 6x + (3 * x + x * x))
30 + 9x = 3(18 + 6x + (3x + x2))

Combine like terms: 6x + 3x = 9x
30 + 9x = 3(18 + 9x + x2)
30 + 9x = (18 * 3 + 9x * 3 + x2 * 3)
30 + 9x = (54 + 27x + 3x2)

Solving
30 + 9x = 54 + 27x + 3x2

Solving for variable 'x'.

Reorder the terms:
30 + -54 + 9x + -27x + -3x2 = 54 + 27x + 3x2 + -54 + -27x + -3x2

Combine like terms: 30 + -54 = -24
-24 + 9x + -27x + -3x2 = 54 + 27x + 3x2 + -54 + -27x + -3x2

Combine like terms: 9x + -27x = -18x
-24 + -18x + -3x2 = 54 + 27x + 3x2 + -54 + -27x + -3x2

Reorder the terms:
-24 + -18x + -3x2 = 54 + -54 + 27x + -27x + 3x2 + -3x2

Combine like terms: 54 + -54 = 0
-24 + -18x + -3x2 = 0 + 27x + -27x + 3x2 + -3x2
-24 + -18x + -3x2 = 27x + -27x + 3x2 + -3x2

Combine like terms: 27x + -27x = 0
-24 + -18x + -3x2 = 0 + 3x2 + -3x2
-24 + -18x + -3x2 = 3x2 + -3x2

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

Factor out the Greatest Common Factor (GCF), '-3'.
-3(8 + 6x + x2) = 0

Factor a trinomial.
-3((4 + x)(2 + x)) = 0

Ignore the factor -3.

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-4, -2}

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