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

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


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

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

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

Multiply (-1 + 2x) * (-5 + 4x)
3x(-1(-5 + 4x) + 2x * (-5 + 4x)) = 0
3x((-5 * -1 + 4x * -1) + 2x * (-5 + 4x)) = 0
3x((5 + -4x) + 2x * (-5 + 4x)) = 0
3x(5 + -4x + (-5 * 2x + 4x * 2x)) = 0
3x(5 + -4x + (-10x + 8x2)) = 0

Combine like terms: -4x + -10x = -14x
3x(5 + -14x + 8x2) = 0
(5 * 3x + -14x * 3x + 8x2 * 3x) = 0
(15x + -42x2 + 24x3) = 0

Solving
15x + -42x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(5 + -14x + 8x2) = 0

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

Subproblem 3
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {0, 0.5, 1.25}

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