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

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


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

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

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

Multiply (-3 + 2x) * (-2 + 3x)
(-3(-2 + 3x) + 2x * (-2 + 3x)) = 0
((-2 * -3 + 3x * -3) + 2x * (-2 + 3x)) = 0
((6 + -9x) + 2x * (-2 + 3x)) = 0
(6 + -9x + (-2 * 2x + 3x * 2x)) = 0
(6 + -9x + (-4x + 6x2)) = 0

Combine like terms: -9x + -4x = -13x
(6 + -13x + 6x2) = 0

Solving
6 + -13x + 6x2 = 0

Solving for variable 'x'.

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


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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 2
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
Solution
x = {0.6666666667, 1.5}

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