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

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


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

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

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

Multiply (-3 + 2x) * (1 + -5x)
(-3(1 + -5x) + 2x * (1 + -5x)) = 0
((1 * -3 + -5x * -3) + 2x * (1 + -5x)) = 0
((-3 + 15x) + 2x * (1 + -5x)) = 0
(-3 + 15x + (1 * 2x + -5x * 2x)) = 0
(-3 + 15x + (2x + -10x2)) = 0

Combine like terms: 15x + 2x = 17x
(-3 + 17x + -10x2) = 0

Solving
-3 + 17x + -10x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-3 + 2x)' equal to zero and attempt to solve:

Simplifying
-3 + 2x = 0

Solving
-3 + 2x = 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 + 2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2x = 0 + 3
2x = 0 + 3

Combine like terms: 0 + 3 = 3
2x = 3

Divide each side by '2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {1.5, 0.2}

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