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

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


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

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

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

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

Combine like terms: 1x + -20x = -19x
X(-5 + -19x + 4x2) = 0
(-5 * X + -19x * X + 4x2 * X) = 0
(-5X + -19xX + 4x2X) = 0

Solving
-5X + -19xX + 4x2X = 0

Solving for variable 'X'.

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

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

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

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

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

Simplifying
0 = 1 + 4x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

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

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

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

Add 'x' to each side of the equation.
-1x + x = -5 + x

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

Simplifying
0 = -5 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
X = {0}

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