X^2(x-4)(2x+5)=0

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


Simplifying
X2(x + -4)(2x + 5) = 0

Reorder the terms:
X2(-4 + x)(2x + 5) = 0

Reorder the terms:
X2(-4 + x)(5 + 2x) = 0

Multiply (-4 + x) * (5 + 2x)
X2(-4(5 + 2x) + x(5 + 2x)) = 0
X2((5 * -4 + 2x * -4) + x(5 + 2x)) = 0
X2((-20 + -8x) + x(5 + 2x)) = 0
X2(-20 + -8x + (5 * x + 2x * x)) = 0
X2(-20 + -8x + (5x + 2x2)) = 0

Combine like terms: -8x + 5x = -3x
X2(-20 + -3x + 2x2) = 0
(-20 * X2 + -3x * X2 + 2x2 * X2) = 0
(-20X2 + -3xX2 + 2x2X2) = 0

Solving
-20X2 + -3xX2 + 2x2X2 = 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), 'X2'.
X2(-20 + -3x + 2x2) = 0

Factor a trinomial.
X2((-5 + -2x)(4 + -1x)) = 0


Subproblem 1
Set the factor 'X2' equal to zero and attempt to solve:

Simplifying
X2 = 0

Solving
X2 = 0

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

Simplifying
X2 = 0

Take the square root of each side:
X = {0}

Subproblem 2
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.

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

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

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

Simplifying
0 = -4 + 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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