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

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


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

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

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

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

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

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

Solving
-2x + 3x2 + 20x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2 + 3x + 20x2) = 0

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


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 '(-2 + -5x)' equal to zero and attempt to solve:

Simplifying
-2 + -5x = 0

Solving
-2 + -5x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5x = 0 + 2
-5x = 0 + 2

Combine like terms: 0 + 2 = 2
-5x = 2

Divide each side by '-5'.
x = -0.4

Simplifying
x = -0.4

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, -0.4, 0.25}

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