9(9+(3x+2))=(x-3)((x-3)+(2x+9))

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Solution for 9(9+(3x+2))=(x-3)((x-3)+(2x+9)) equation: 


Simplifying
9(9 + (3x + 2)) = (x + -3)((x + -3) + (2x + 9))

Reorder the terms:
9(9 + (2 + 3x)) = (x + -3)((x + -3) + (2x + 9))

Remove parenthesis around (2 + 3x)
9(9 + 2 + 3x) = (x + -3)((x + -3) + (2x + 9))

Combine like terms: 9 + 2 = 11
9(11 + 3x) = (x + -3)((x + -3) + (2x + 9))
(11 * 9 + 3x * 9) = (x + -3)((x + -3) + (2x + 9))
(99 + 27x) = (x + -3)((x + -3) + (2x + 9))

Reorder the terms:
99 + 27x = (-3 + x)((x + -3) + (2x + 9))

Reorder the terms:
99 + 27x = (-3 + x)((-3 + x) + (2x + 9))

Remove parenthesis around (-3 + x)
99 + 27x = (-3 + x)(-3 + x + (2x + 9))

Reorder the terms:
99 + 27x = (-3 + x)(-3 + x + (9 + 2x))

Remove parenthesis around (9 + 2x)
99 + 27x = (-3 + x)(-3 + x + 9 + 2x)

Reorder the terms:
99 + 27x = (-3 + x)(-3 + 9 + x + 2x)

Combine like terms: -3 + 9 = 6
99 + 27x = (-3 + x)(6 + x + 2x)

Combine like terms: x + 2x = 3x
99 + 27x = (-3 + x)(6 + 3x)

Multiply (-3 + x) * (6 + 3x)
99 + 27x = (-3(6 + 3x) + x(6 + 3x))
99 + 27x = ((6 * -3 + 3x * -3) + x(6 + 3x))
99 + 27x = ((-18 + -9x) + x(6 + 3x))
99 + 27x = (-18 + -9x + (6 * x + 3x * x))
99 + 27x = (-18 + -9x + (6x + 3x2))

Combine like terms: -9x + 6x = -3x
99 + 27x = (-18 + -3x + 3x2)

Solving
99 + 27x = -18 + -3x + 3x2

Solving for variable 'x'.

Reorder the terms:
99 + 18 + 27x + 3x + -3x2 = -18 + -3x + 3x2 + 18 + 3x + -3x2

Combine like terms: 99 + 18 = 117
117 + 27x + 3x + -3x2 = -18 + -3x + 3x2 + 18 + 3x + -3x2

Combine like terms: 27x + 3x = 30x
117 + 30x + -3x2 = -18 + -3x + 3x2 + 18 + 3x + -3x2

Reorder the terms:
117 + 30x + -3x2 = -18 + 18 + -3x + 3x + 3x2 + -3x2

Combine like terms: -18 + 18 = 0
117 + 30x + -3x2 = 0 + -3x + 3x + 3x2 + -3x2
117 + 30x + -3x2 = -3x + 3x + 3x2 + -3x2

Combine like terms: -3x + 3x = 0
117 + 30x + -3x2 = 0 + 3x2 + -3x2
117 + 30x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
117 + 30x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(39 + 10x + -1x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 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 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
Solution
x = {13, -3}

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