3(2x-3)(x-3)=0

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Solution for 3(2x-3)(x-3)=0 equation: 


Simplifying
3(2x + -3)(x + -3) = 0

Reorder the terms:
3(-3 + 2x)(x + -3) = 0

Reorder the terms:
3(-3 + 2x)(-3 + x) = 0

Multiply (-3 + 2x) * (-3 + x)
3(-3(-3 + x) + 2x * (-3 + x)) = 0
3((-3 * -3 + x * -3) + 2x * (-3 + x)) = 0
3((9 + -3x) + 2x * (-3 + x)) = 0
3(9 + -3x + (-3 * 2x + x * 2x)) = 0
3(9 + -3x + (-6x + 2x2)) = 0

Combine like terms: -3x + -6x = -9x
3(9 + -9x + 2x2) = 0
(9 * 3 + -9x * 3 + 2x2 * 3) = 0
(27 + -27x + 6x2) = 0

Solving
27 + -27x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + -9x + 2x2) = 0

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

Ignore the factor 3.

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
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
Solution
x = {1.5, 3}

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