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

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


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

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

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

Multiply (-5 + 2x) * (1 + 2x)
X(-5(1 + 2x) + 2x * (1 + 2x)) = 0
X((1 * -5 + 2x * -5) + 2x * (1 + 2x)) = 0
X((-5 + -10x) + 2x * (1 + 2x)) = 0
X(-5 + -10x + (1 * 2x + 2x * 2x)) = 0
X(-5 + -10x + (2x + 4x2)) = 0

Combine like terms: -10x + 2x = -8x
X(-5 + -8x + 4x2) = 0
(-5 * X + -8x * X + 4x2 * X) = 0
(-5X + -8xX + 4x2X) = 0

Solving
-5X + -8xX + 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 + -8x + 4x2) = 0

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Add '2x' to each side of the equation.
-2x + 2x = 1 + 2x

Combine like terms: -2x + 2x = 0
0 = 1 + 2x

Simplifying
0 = 1 + 2x

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 + -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

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

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

Simplifying
0 = -5 + 2x

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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