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

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


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

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

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

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

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

Multiply (-3 + x) * (6 + 3x)
(-3(6 + 3x) + x(6 + 3x)) = 9(9 + 3x + 2)
((6 * -3 + 3x * -3) + x(6 + 3x)) = 9(9 + 3x + 2)
((-18 + -9x) + x(6 + 3x)) = 9(9 + 3x + 2)
(-18 + -9x + (6 * x + 3x * x)) = 9(9 + 3x + 2)
(-18 + -9x + (6x + 3x2)) = 9(9 + 3x + 2)

Combine like terms: -9x + 6x = -3x
(-18 + -3x + 3x2) = 9(9 + 3x + 2)

Reorder the terms:
-18 + -3x + 3x2 = 9(9 + 2 + 3x)

Combine like terms: 9 + 2 = 11
-18 + -3x + 3x2 = 9(11 + 3x)
-18 + -3x + 3x2 = (11 * 9 + 3x * 9)
-18 + -3x + 3x2 = (99 + 27x)

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

Solving for variable 'x'.

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

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

Combine like terms: -3x + -27x = -30x
-117 + -30x + 3x2 = 99 + 27x + -99 + -27x

Reorder the terms:
-117 + -30x + 3x2 = 99 + -99 + 27x + -27x

Combine like terms: 99 + -99 = 0
-117 + -30x + 3x2 = 0 + 27x + -27x
-117 + -30x + 3x2 = 27x + -27x

Combine like terms: 27x + -27x = 0
-117 + -30x + 3x2 = 0

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

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

Ignore the factor 3.

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
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
Solution
x = {-3, 13}

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