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

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


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

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

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

Multiply (-1 + 2x) * (-5 + 3x)
4x(-1(-5 + 3x) + 2x * (-5 + 3x)) = 0
4x((-5 * -1 + 3x * -1) + 2x * (-5 + 3x)) = 0
4x((5 + -3x) + 2x * (-5 + 3x)) = 0
4x(5 + -3x + (-5 * 2x + 3x * 2x)) = 0
4x(5 + -3x + (-10x + 6x2)) = 0

Combine like terms: -3x + -10x = -13x
4x(5 + -13x + 6x2) = 0
(5 * 4x + -13x * 4x + 6x2 * 4x) = 0
(20x + -52x2 + 24x3) = 0

Solving
20x + -52x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(5 + -13x + 6x2) = 0

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

Ignore the factor 4.

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 + -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
Solution
x = {0, 0.5, 1.666666667}

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