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

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


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

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

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

Multiply (-5 + 3x) * (5 + -2x)
2(-5(5 + -2x) + 3x * (5 + -2x)) = 0
2((5 * -5 + -2x * -5) + 3x * (5 + -2x)) = 0
2((-25 + 10x) + 3x * (5 + -2x)) = 0
2(-25 + 10x + (5 * 3x + -2x * 3x)) = 0
2(-25 + 10x + (15x + -6x2)) = 0

Combine like terms: 10x + 15x = 25x
2(-25 + 25x + -6x2) = 0
(-25 * 2 + 25x * 2 + -6x2 * 2) = 0
(-50 + 50x + -12x2) = 0

Solving
-50 + 50x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 25x + -6x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {2.5, 1.666666667}

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