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

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


Simplifying
2x(3 + -1x)(2x + -5) = 0

Reorder the terms:
2x(3 + -1x)(-5 + 2x) = 0

Multiply (3 + -1x) * (-5 + 2x)
2x(3(-5 + 2x) + -1x * (-5 + 2x)) = 0
2x((-5 * 3 + 2x * 3) + -1x * (-5 + 2x)) = 0
2x((-15 + 6x) + -1x * (-5 + 2x)) = 0
2x(-15 + 6x + (-5 * -1x + 2x * -1x)) = 0
2x(-15 + 6x + (5x + -2x2)) = 0

Combine like terms: 6x + 5x = 11x
2x(-15 + 11x + -2x2) = 0
(-15 * 2x + 11x * 2x + -2x2 * 2x) = 0
(-30x + 22x2 + -4x3) = 0

Solving
-30x + 22x2 + -4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-15 + 11x + -2x2) = 0

Factor a trinomial.
2x((-3 + x)(5 + -2x)) = 0

Ignore the factor 2.

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 '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

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

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

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

Simplifying
x = 3

Subproblem 3
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, 3, 2.5}

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