(-9x-3)(-6x-6)-27x-9=0

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Solution for (-9x-3)(-6x-6)-27x-9=0 equation: 


Simplifying
(-9x + -3)(-6x + -6) + -27x + -9 = 0

Reorder the terms:
(-3 + -9x)(-6x + -6) + -27x + -9 = 0

Reorder the terms:
(-3 + -9x)(-6 + -6x) + -27x + -9 = 0

Multiply (-3 + -9x) * (-6 + -6x)
(-3(-6 + -6x) + -9x * (-6 + -6x)) + -27x + -9 = 0
((-6 * -3 + -6x * -3) + -9x * (-6 + -6x)) + -27x + -9 = 0
((18 + 18x) + -9x * (-6 + -6x)) + -27x + -9 = 0
(18 + 18x + (-6 * -9x + -6x * -9x)) + -27x + -9 = 0
(18 + 18x + (54x + 54x2)) + -27x + -9 = 0

Combine like terms: 18x + 54x = 72x
(18 + 72x + 54x2) + -27x + -9 = 0

Reorder the terms:
18 + -9 + 72x + -27x + 54x2 = 0

Combine like terms: 18 + -9 = 9
9 + 72x + -27x + 54x2 = 0

Combine like terms: 72x + -27x = 45x
9 + 45x + 54x2 = 0

Solving
9 + 45x + 54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(1 + 5x + 6x2) = 0

Factor a trinomial.
9((1 + 2x)(1 + 3x)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {-0.5, -0.3333333333}

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