(3x-2)(2x-5)=0

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Solution for (3x-2)(2x-5)=0 equation: 


Simplifying
(3x + -2)(2x + -5) = 0

Reorder the terms:
(-2 + 3x)(2x + -5) = 0

Reorder the terms:
(-2 + 3x)(-5 + 2x) = 0

Multiply (-2 + 3x) * (-5 + 2x)
(-2(-5 + 2x) + 3x * (-5 + 2x)) = 0
((-5 * -2 + 2x * -2) + 3x * (-5 + 2x)) = 0
((10 + -4x) + 3x * (-5 + 2x)) = 0
(10 + -4x + (-5 * 3x + 2x * 3x)) = 0
(10 + -4x + (-15x + 6x2)) = 0

Combine like terms: -4x + -15x = -19x
(10 + -19x + 6x2) = 0

Solving
10 + -19x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -3x)(5 + -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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0.6666666667, 2.5}

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