(3-6x)(2x-5)=0

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Solution for (3-6x)(2x-5)=0 equation: 


Simplifying
(3 + -6x)(2x + -5) = 0

Reorder the terms:
(3 + -6x)(-5 + 2x) = 0

Multiply (3 + -6x) * (-5 + 2x)
(3(-5 + 2x) + -6x * (-5 + 2x)) = 0
((-5 * 3 + 2x * 3) + -6x * (-5 + 2x)) = 0
((-15 + 6x) + -6x * (-5 + 2x)) = 0
(-15 + 6x + (-5 * -6x + 2x * -6x)) = 0
(-15 + 6x + (30x + -12x2)) = 0

Combine like terms: 6x + 30x = 36x
(-15 + 36x + -12x2) = 0

Solving
-15 + 36x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 12x + -4x2) = 0

Factor a trinomial.
3((-5 + 2x)(1 + -2x)) = 0

Ignore the factor 3.

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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {2.5, 0.5}

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