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

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


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

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

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

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

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

Solving
-1X + 4xX + 5x2X = 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(-1 + 4x + 5x2) = 0

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

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

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

Simplifying
0 = 1 + x

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 '(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

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

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

Simplifying
0 = -1 + 5x

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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