-9(x+6)-6(x+9)=(-6x-54)(x+6)

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Solution for -9(x+6)-6(x+9)=(-6x-54)(x+6) equation: 


Simplifying
-9(x + 6) + -6(x + 9) = (-6x + -54)(x + 6)

Reorder the terms:
-9(6 + x) + -6(x + 9) = (-6x + -54)(x + 6)
(6 * -9 + x * -9) + -6(x + 9) = (-6x + -54)(x + 6)
(-54 + -9x) + -6(x + 9) = (-6x + -54)(x + 6)

Reorder the terms:
-54 + -9x + -6(9 + x) = (-6x + -54)(x + 6)
-54 + -9x + (9 * -6 + x * -6) = (-6x + -54)(x + 6)
-54 + -9x + (-54 + -6x) = (-6x + -54)(x + 6)

Reorder the terms:
-54 + -54 + -9x + -6x = (-6x + -54)(x + 6)

Combine like terms: -54 + -54 = -108
-108 + -9x + -6x = (-6x + -54)(x + 6)

Combine like terms: -9x + -6x = -15x
-108 + -15x = (-6x + -54)(x + 6)

Reorder the terms:
-108 + -15x = (-54 + -6x)(x + 6)

Reorder the terms:
-108 + -15x = (-54 + -6x)(6 + x)

Multiply (-54 + -6x) * (6 + x)
-108 + -15x = (-54(6 + x) + -6x * (6 + x))
-108 + -15x = ((6 * -54 + x * -54) + -6x * (6 + x))
-108 + -15x = ((-324 + -54x) + -6x * (6 + x))
-108 + -15x = (-324 + -54x + (6 * -6x + x * -6x))
-108 + -15x = (-324 + -54x + (-36x + -6x2))

Combine like terms: -54x + -36x = -90x
-108 + -15x = (-324 + -90x + -6x2)

Solving
-108 + -15x = -324 + -90x + -6x2

Solving for variable 'x'.

Reorder the terms:
-108 + 324 + -15x + 90x + 6x2 = -324 + -90x + -6x2 + 324 + 90x + 6x2

Combine like terms: -108 + 324 = 216
216 + -15x + 90x + 6x2 = -324 + -90x + -6x2 + 324 + 90x + 6x2

Combine like terms: -15x + 90x = 75x
216 + 75x + 6x2 = -324 + -90x + -6x2 + 324 + 90x + 6x2

Reorder the terms:
216 + 75x + 6x2 = -324 + 324 + -90x + 90x + -6x2 + 6x2

Combine like terms: -324 + 324 = 0
216 + 75x + 6x2 = 0 + -90x + 90x + -6x2 + 6x2
216 + 75x + 6x2 = -90x + 90x + -6x2 + 6x2

Combine like terms: -90x + 90x = 0
216 + 75x + 6x2 = 0 + -6x2 + 6x2
216 + 75x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
216 + 75x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(72 + 25x + 2x2) = 0

Factor a trinomial.
3((8 + x)(9 + 2x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(9 + 2x)' equal to zero and attempt to solve:

Simplifying
9 + 2x = 0

Solving
9 + 2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2x = 0 + -9
2x = 0 + -9

Combine like terms: 0 + -9 = -9
2x = -9

Divide each side by '2'.
x = -4.5

Simplifying
x = -4.5
Solution
x = {-8, -4.5}

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