(3x-21)(x-5)=9

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Solution for (3x-21)(x-5)=9 equation: 


Simplifying
(3x + -21)(x + -5) = 9

Reorder the terms:
(-21 + 3x)(x + -5) = 9

Reorder the terms:
(-21 + 3x)(-5 + x) = 9

Multiply (-21 + 3x) * (-5 + x)
(-21(-5 + x) + 3x * (-5 + x)) = 9
((-5 * -21 + x * -21) + 3x * (-5 + x)) = 9
((105 + -21x) + 3x * (-5 + x)) = 9
(105 + -21x + (-5 * 3x + x * 3x)) = 9
(105 + -21x + (-15x + 3x2)) = 9

Combine like terms: -21x + -15x = -36x
(105 + -36x + 3x2) = 9

Solving
105 + -36x + 3x2 = 9

Solving for variable 'x'.

Reorder the terms:
105 + -9 + -36x + 3x2 = 9 + -9

Combine like terms: 105 + -9 = 96
96 + -36x + 3x2 = 9 + -9

Combine like terms: 9 + -9 = 0
96 + -36x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(32 + -12x + x2) = 0

Factor a trinomial.
3((4 + -1x)(8 + -1x)) = 0

Ignore the factor 3.

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {4, 8}

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