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

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


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

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

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

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

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

Add '-9' to each side of the equation.
9 + -9x + -9 + 2x2 = 9 + -9

Reorder the terms:
9 + -9 + -9x + 2x2 = 9 + -9

Combine like terms: 9 + -9 = 0
0 + -9x + 2x2 = 9 + -9
-9x + 2x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9x + 2x2 = 0

Solving
-9x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-9 + 2x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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 = {0, 4.5}

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