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

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


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

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

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

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

Combine like terms: 15x + 2x = 17x
(-5 + 17x + -6x2) = 0

Solving
-5 + 17x + -6x2 = 0

Solving for variable 'x'.

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


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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {2.5, 0.3333333333}

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