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

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


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

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

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

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

Combine like terms: -5x + -2x = -7x
4x(5 + -7x + 2x2) = 0
(5 * 4x + -7x * 4x + 2x2 * 4x) = 0
(20x + -28x2 + 8x3) = 0

Solving
20x + -28x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(5 + -7x + 2x2) = 0

Factor a trinomial.
4x((1 + -1x)(5 + -2x)) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 3
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
Solution
x = {0, 1, 2.5}

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