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

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


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

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

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

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

Combine like terms: -20x + 1x = -19x
5x(-4 + -19x + 5x2) = 0
(-4 * 5x + -19x * 5x + 5x2 * 5x) = 0
(-20x + -95x2 + 25x3) = 0

Solving
-20x + -95x2 + 25x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-4 + -19x + 5x2) = 0

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

Ignore the factor 5.

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

Simplifying
-1 + -5x = 0

Solving
-1 + -5x = 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 + -5x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5x = 0 + 1
-5x = 0 + 1

Combine like terms: 0 + 1 = 1
-5x = 1

Divide each side by '-5'.
x = -0.2

Simplifying
x = -0.2

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, -0.2, 4}

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