3x(4x-1)(-2x+5)=0

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Solution for 3x(4x-1)(-2x+5)=0 equation: 


Simplifying
3x(4x + -1)(-2x + 5) = 0

Reorder the terms:
3x(-1 + 4x)(-2x + 5) = 0

Reorder the terms:
3x(-1 + 4x)(5 + -2x) = 0

Multiply (-1 + 4x) * (5 + -2x)
3x(-1(5 + -2x) + 4x * (5 + -2x)) = 0
3x((5 * -1 + -2x * -1) + 4x * (5 + -2x)) = 0
3x((-5 + 2x) + 4x * (5 + -2x)) = 0
3x(-5 + 2x + (5 * 4x + -2x * 4x)) = 0
3x(-5 + 2x + (20x + -8x2)) = 0

Combine like terms: 2x + 20x = 22x
3x(-5 + 22x + -8x2) = 0
(-5 * 3x + 22x * 3x + -8x2 * 3x) = 0
(-15x + 66x2 + -24x3) = 0

Solving
-15x + 66x2 + -24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-5 + 22x + -8x2) = 0

Factor a trinomial.
3x((-5 + 2x)(1 + -4x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
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 3
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {0, 2.5, 0.25}

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