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

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


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

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

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

Multiply (-2 + 5x) * (5 + 2x)
x(-2(5 + 2x) + 5x * (5 + 2x)) = 0
x((5 * -2 + 2x * -2) + 5x * (5 + 2x)) = 0
x((-10 + -4x) + 5x * (5 + 2x)) = 0
x(-10 + -4x + (5 * 5x + 2x * 5x)) = 0
x(-10 + -4x + (25x + 10x2)) = 0

Combine like terms: -4x + 25x = 21x
x(-10 + 21x + 10x2) = 0
(-10 * x + 21x * x + 10x2 * x) = 0
(-10x + 21x2 + 10x3) = 0

Solving
-10x + 21x2 + 10x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-10 + 21x + 10x2) = 0

Factor a trinomial.
x((-5 + -2x)(2 + -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 '(-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

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 3
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

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

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

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {0, -2.5, 0.4}

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