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

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Solution for (2x-1)(5-3x)=0 equation: 


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

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

Multiply (-1 + 2x) * (5 + -3x)
(-1(5 + -3x) + 2x * (5 + -3x)) = 0
((5 * -1 + -3x * -1) + 2x * (5 + -3x)) = 0
((-5 + 3x) + 2x * (5 + -3x)) = 0
(-5 + 3x + (5 * 2x + -3x * 2x)) = 0
(-5 + 3x + (10x + -6x2)) = 0

Combine like terms: 3x + 10x = 13x
(-5 + 13x + -6x2) = 0

Solving
-5 + 13x + -6x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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 = {1.666666667, 0.5}

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